arc - a portion of the boundary of a circle or a curve

-28 is the solution to the sum of a number p and 21

-28 is the solution to the sum of a number p and 21
The sum of a number p and 21:
p + 21
The phrase [I]is the solution to[/I] means an equation, so we set p + 21 equal to -28:
[B]p + 21 = -28
[/B]
If the problem asks you to solve for p, then we [URL='https://www.mathcelebrity.com/1unk.php?num=p%2B21%3D-28&pl=Solve']type this into our search engine[/URL] and we get:
p = [B]-49[/B]

-65 times the difference between a number and 79 is equal to the number plus 98

-65 times the difference between a number and 79 is equal to the number plus 98
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
The first expression, [I]the difference between a number and 79[/I] means we subtract 79 from our arbitrary variable of x:
x - 79
Next, -65 times the difference between a number and 79 means we multiply our result above by -65:
-65(x - 79)
The phrase [I]the number[/I] refers to the arbitrary variable x earlier. The number plus 98 means we add 98 to x:
x + 98
Now, let's bring it all together. The phrase [I]is equal to[/I] means an equation. So we set -65(x - 79) equal to x + [B]98:
-65(x - 79) = x + 98[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=-65%28x-79%29%3Dx%2B98&pl=Solve']type this equation into our search engine[/URL], and you get:
x = [B]76.31818[/B]

1 box is used every 1.5 days. How many are used in 242 days?

1 box is used every 1.5 days. How many are used in 242 days?
Set up a proportion of boxes to days where b is the number of boxes used for 242 days:
1/1.5 = b/242
To solve this proportion for b, we [URL='https://www.mathcelebrity.com/prop.php?num1=1&num2=b&den1=1.5&den2=242&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
b = [B]161.3333[/B]

1 year from now Mike will be 40 years old. The current sum of the ages of Mike and John is 89. How o

1 year from now Mike will be 40 years old. The current sum of the ages of Mike and John is 89. How old is John right now?
If Mike will be 40 1 year from now, then he is:
40 - 1 = 39 years old today.
And if the current sum of Mike and John's age is 89, then we use j for John's age:
j + 39 = 89
[URL='https://www.mathcelebrity.com/1unk.php?num=j%2B39%3D89&pl=Solve']Type this equation into our search engine[/URL], and we get:
[B]j = 50[/B]

1 year from now Paul will be 49 years old. The current sum of the ages of Paul and Sharon is 85. How

1 year from now Paul will be 49 years old. The current sum of the ages of Paul and Sharon is 85. How old is Sharon right now?
If Paul will be 49 years old 1 year from now, this means today, he is 49 - 1 = 48 years old.
Let Sharon's age be s. Then from the current sum of Paul and Sharon's ages, we get:
s + 49 = 85
[URL='https://www.mathcelebrity.com/1unk.php?num=s%2B49%3D85&pl=Solve']Type this equation into our search engine[/URL], and get:
s = [B]36[/B]

1/3 of students at a school are boys. If there are 600 students at the school, how many are girls?

1/3 of students at a school are boys. If there are 600 students at the school, how many are girls?
If 1/3 are boys, then the number of boys is:
600 * 1/3
600/3
We [URL='https://www.mathcelebrity.com/fraction.php?frac1=600%2F3&frac2=3%2F8&pl=Simplify']type this fraction into our search engine to simplify[/URL], and we get:
200
Now we need to find how many girls are at the school:
Girls = Total Students - Boys
Girls = 600 - 200
Girls = [B]400[/B]

1/9 of all sales were for cash. If cash sales were $59,000, what were the total sales?

1/9 of all sales were for cash. If cash sales were $59,000, what were the total sales?
Let sales be s. We're given:
s/9 = 59000
To solve this proportion for s, we [URL='https://www.mathcelebrity.com/prop.php?num1=s&num2=59000&den1=9&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
s = [B]531000[/B]

10 times the first of 2 consecutive even integers is 8 times the second. Find the integers

10 times the first of 2 consecutive even integers is 8 times the second. Find the integers.
Let the first integer be x. Let the second integer be y. We're given:
[LIST=1]
[*]10x = 8y
[*]We also know a consecutive even integer means we add 2 to x to get y. y = x + 2
[/LIST]
Substitute (1) into (2):
10x = 8(x + 2)
Multiply through:
10x = 8x + 16
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=10x%3D8x%2B16&pl=Solve']we type this equation into our search engine[/URL] and we get:
[B]x = 8[/B]
Since y = x + 2, we plug in x = 8 to get:
y = 8 + 2
[B]y = 10
[/B]
Now, let's check our work. Does x = 8 and y = 10 make equation 1 hold?
10(8) ? 8(10)
80 = 80 <-- Yes!

10% of the days in June were sunny. How many days in June were sunny?

10% of the days in June were sunny. How many days in June were sunny?
June has 30 days.
We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=10&den1=30&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type in 10% of 30[/URL] in our search engine:
[B]3 days[/B]

12 plus 6 times a number is 9 times the number

12 plus 6 times a number is 9 times the number
The phrase [I]a number [/I]means an arbitrary variable. Let's call it x.
6 times a number is written as:
6x
12 plus 6 times the number means we add 6x to 12:
12 + 6x
9 times a number is written as:
9x
The phrase [I]is[/I] means an equation, so we set 12 + 6x equal to 9x
[B]12 + 6x = 9x <-- This is our algebraic expression[/B]
[B][/B]
If the problem asks you to solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B6x%3D9x&pl=Solve']type this expression into our search engine[/URL] and you get:
x = [B]4[/B]

12 students want pancakes and 14 students want waffles. What is the ratio of the number of students

12 students want pancakes and 14 students want waffles. What is the ratio of the number of students who want pancakes to the total number of students?
12/14 is the initial ratio. However, we can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=12%2F14&frac2=3%2F8&pl=Simplify']So we type 12/14 into our search engine and choose simplify.[/URL] We get:
6/7

1225 people live in a village,329 are men and 404 are women. how many are children

1225 people live in a village,329 are men and 404 are women. how many are children
We can have either men, women, or children. We have the following equation where children are "c".
239 + 404 + c = 1225
To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=239%2B404%2Bc%3D1225&pl=Solve']type this equation into our search engine[/URL] and we get:
c = [B]582[/B]

13 minutes to answer 4 problems. how many minutes would it take to answer 22 questions

13 minutes to answer 4 problems. how many minutes would it take to answer 22 questions?
Set up a proportion of time to problems where m is the number of minutes it would take for 22 questions:
13/4 = m/22
[URL='https://www.mathcelebrity.com/prop.php?num1=13&num2=m&den1=4&den2=22&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get:
m = [B]71.5[/B]

14 oranges $3.78

14 oranges $3.78
Using our [URL='http://www.mathcelebrity.com/unit-cost-calculator.php?num=14orangesfor3.78&pl=Calculate+Unit+Cost']unit cost calculator[/URL], we get:
[B]$0.27 per orange[/B].
You could also enter in the search engine:
14 oranges for $3.78

15 mins into fraction of an hour

15 mins into fraction of an hour
[URL='https://www.mathcelebrity.com/timecon.php?quant=1&pl=Calculate&type=hour']An hour is 60 minutes[/URL], so we have the fraction:
15/60
But we can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=15%2F60&frac2=3%2F8&pl=Simplify']type in 15/60 into our search engine[/URL], click Simplify, and we get:
[B]1/4[/B]

165cm in ft

Using our [URL='http://www.mathcelebrity.com/linearcon.php?quant=165&pl=Calculate&type=centimeter#foot']linear conversion calculator[/URL], we get:
[B]5.41339 feet[/B]

2 buses leave at 5:30am, 1 comes every 18 minutes and one comes every 15 minutes when will they both

2 buses leave at 5:30am, 1 comes every 18 minutes and one comes every 15 minutes when will they both come at the same time again
We want the Least Common Multiple (LCM) of 15 and 18. LCM(15, 18)
Enter this into the [URL='http://www.mathcelebrity.com/gcflcm.php?num1=15&num2=18&num3=&pl=LCM']search engine[/URL], and we get:
[B]90 minutes[/B]

2 cards have different expressions written on them.: 5y - 2 and 3y + 10. for what value of y do the

2 cards have different expressions written on them.: 5y - 2 and 3y + 10. for what value of y do the 2 cards represent the same number?
If they have the same number, we set them equal to each other and solve for y:
5y - 2 = 3y + 10
To solve for y, we [URL='http://5y - 2 = 3y + 10']type this expression in our search engine [/URL]and we get:
y = [B]6[/B]

2 consecutive odd integers such that their product is 15 more than 3 times their sum

2 consecutive odd integers such that their product is 15 more than 3 times their sum.
Let the first integer be n. The next odd, consecutive integer is n + 2.
We are given the product is 15 more than 3 times their sum:
n(n + 2) = 3(n + n + 2) + 15
Simplify each side:
n^2 + 2n = 6n + 6 + 15
n^2 + 2n = 6n + 21
Subtract 6n from each side:
n^2 - 4n - 21 = 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-4n-21%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get:
n = (-3, 7)
If we use -3, then the next consecutive odd integer is -3 + 2 = -1. So we have [B](-3, -1)[/B]
If we use 7, then the next consecutive odd integer is 7 + 2 = 9. So we have [B](7, 9)[/B]

2 numbers add to 200. The first is 20 less than the second.

2 numbers add to 200. The first is 20 less than the second.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]x + y = 200
[*]x = y - 20
[/LIST]
Plug (2) into (1)
(y - 20) + y = 200
Group like terms:
2y - 20 = 200
[URL='https://www.mathcelebrity.com/1unk.php?num=2y-20%3D200&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 110[/B] <-- This is the larger number
Plug y = 110 into Equation (2) to get the smaller number:
x = 110 - 20
[B]x = 90[/B] <-- This is the smaller number
Let's check our work for Equation (1) using x = 90, and y = 110
90 + 110 ? 200
200 = 200 <-- Good, our solutions check out for equation (1)
Let's check our work for Equation (2) using x = 90, and y = 110
90 = 110 - 20
90 = 90 <-- Good, our solutions check out for equation (2)

2 numbers that add up makes 5 but multiplied makes -36

2 numbers that add up makes 5 but multiplied makes -36
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*]x + y = 5
[*]xy = -36
[/LIST]
Rearrange equation (1) by subtracting y from each side:
[LIST=1]
[*]x = 5 - y
[*]xy = -36
[/LIST]
Substitute equation (1) for x into equation (2):
(5 - y)y = -36
5y - y^2 = -36
Add 36 to each side:
-y^2 + 5y + 36 = 0
We have a quadratic equation. To solve this, we [URL='https://www.mathcelebrity.com/quadratic.php?num=-y%5E2%2B5y%2B36%3D0&pl=Solve+Quadratic+Equation&hintnum=0']type it in our search engine and solve[/URL] to get:
y = ([B]-4, 9[/B])
We check our work for each equation:
[LIST=1]
[*]-4 + 9 = -5
[*]-4(9) = -36
[/LIST]
They both check out

2 times a number added to another number is 25. 3 times the first number minus the other number is 2

2 times a number added to another number is 25. 3 times the first number minus the other number is 20.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]2x + y = 25
[*]3x - y = 20
[/LIST]
Since we have matching opposite coefficients for y (1 and -1), we can add both equations together and eliminate a variable.
(2 + 3)x + (1 - 1)y = 25 + 20
Simplifying, we get:
5x = 45
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D45&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]x = 9[/B]
To find y, we plug in x = 9 into equation (1) or (2). Let's choose equation (1):
2(9) + y = 25
y + 18 = 25
[URL='https://www.mathcelebrity.com/1unk.php?num=y%2B18%3D25&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 7[/B]
So we have (x, y) = (9, 7)
Let's check our work for equation (2) to make sure this system works:
3(9) - 7 ? 20
27 - 7 ? 20
20 = 20 <-- Good, we match!

2 times a number equals that number plus 5

2 times a number equals that number plus 5
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
2 times a number means we multiply 2 by x:
2x
That number plus 5 means we add 5 to the number x
x + 5
The phrase [I]equals[/I] means we set both expressions equal to each other
[B]2x = x + 5[/B] <-- This is our algebraic expression
If you want to take this further and solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3Dx%2B5&pl=Solve']type this expression in the search engine[/URL] and we get:
[B]x = 5[/B]

2 times as many dimes as quarters and they have a combined value of 180 cents, how many of each coin

2 times as many dimes as quarters and they have a combined value of 180 cents, how many of each coin does he have?
Let d be the number of dimes. Let q be the number of quarters. We're given two equations:
[LIST=1]
[*]d = 2q
[*]0.1d + 0.25q = 180
[/LIST]
Substitute (1) into (2):
0.1(2q) + 0.25q = 180
0.2q + 0.25q = 180
[URL='https://www.mathcelebrity.com/1unk.php?num=0.2q%2B0.25q%3D180&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]q = 400[/B]
Now substitute q = 400 into equation 1:
d = 2(400)
[B]d = 800[/B]

2 times the sum of 3 and 5 divided by 10

2 times the sum of 3 and 5 divided by 10
The sum of 3 and 5 is written as:
3 + 5
2 times this sum:
2(3 + 5)
Then, we divide this by 10:
[B]2(3 + 5)/10[/B]
[B][/B]
If the problem asks you to simplify this, you [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=2%283%2B5%29%2F10&pl=Perform+Order+of+Operations']type this expression into our search engine[/URL] and get:
[B]1.6[/B]

2 tons of dirt cost $280.00. What is the price per pound?

2 tons of dirt cost $280.00. What is the price per pound?
We know that 1 ton = 2000 pounds.
So 2 tons = 2*2000 = 4,000 pounds
We rewrite this as 4,000 pounds of dirt cost $280.00.
We set up a proportion where p is the price per one pound:
4000/280 = 1/p
[URL='https://www.mathcelebrity.com/prop.php?num1=4000&num2=1&den1=280&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Plugging this in our search engine[/URL], we get:
p = [B]0.07 or 7 cents per pound.[/B]

20 percent of my class is boys. There are 30 boys in class. How many girls in my class

20 percent of my class is boys. There are 30 boys in class. How many girls in my class?
Let c be the number of people in class. Since 20% = 0.2, We're given:
0.2c = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=0.2c%3D30&pl=Solve']Type this equation into our search engine[/URL], we get:
c = 150
Since the class is made up of boys and girls, we find the number of girls in the class by this equation:
Girls = 150 - 30
Girls = [B]120[/B]

2000 people attended a baseball game 1300 of the people attending supported the home team while 700

2000 people attended a baseball game 1300 of the people attending supported the home team while 700 supported the visiting team what percentage of people attending supported the home team
We want the percentage of 1300 out of 2000.
[URL='https://www.mathcelebrity.com/perc.php?num=1300&den=2000&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']We go to our search engine and type 1300 out of 2300 as a percent[/URL] and we get:
[B]65%[/B]

231 is 248 subtracted from the quantity h times 128

231 is 248 subtracted from the quantity h times 128
Let's take this algebraic expression in parts:
[LIST=1]
[*]h times 128: 128h
[*]24 subtracted from this: 128h - 248
[*]The word [I]is[/I] means an equation, so we set 128h - 248 equal to 231
[/LIST]
[B]128h - 248 = 231[/B] <-- This is our algebraic expression
If the problem asks you to solve for h, then you [URL='https://www.mathcelebrity.com/1unk.php?num=128h-248%3D231&pl=Solve']type in this equation into our search engine[/URL] and get:
h = [B]3.742[/B]

249 equals 191 times c, decreased by 199

249 equals 191 times c, decreased by 199
[U]Take this in pieces:[/U]
191 times c: 191c
The phrase [I]decreased by[/I] means we subtract 199 from 191c: 191c - 199
We set this expression equal to 249:
[B]191c - 199 = 249[/B] <-- This is our algebraic expression
If you want to solve for c, type this equation into the search engine and we get:
[B]c = 2.346[/B]

2consecutiveevenintegerssuchthatthesmalleraddedto5timesthelargergivesasumof70

2 consecutive even integers such that the smaller added to 5 times the larger gives a sum of 70.
Let the first, smaller integer be x. And the second larger integer be y. Since they are both even, we have:
[LIST=1]
[*]x = y - 2 <-- Since they're consecutive even integers
[*]x + 5y = 70 <-- Smaller added to 5 times the larger gives a sum of 70
[/LIST]
Substitute (1) into (2):
(y - 2) + 5y = 70
Group like terms:
(1 + 5)y - 2 = 70
6y - 2 = 70
[URL='https://www.mathcelebrity.com/1unk.php?num=6y-2%3D70&pl=Solve']Typing 6y - 2 = 70 into our search engine[/URL], we get:
[B]y = 12 <-- Larger integer[/B]
Plugging this into Equation (1) we get:
x = 12 - 2
[B]x = 10 <-- Smaller Integer[/B]
So (x, y) = (10, 12)

2x decreased by 15 is equal to -27

2x decreased by 15 is equal to -27
The phrase [I]decreased by[/I] 15 means we subtract 15 from 2x:
2x - 15
The phrase [I]is equal to[/I] means an equation, so we set 2x - 15 equal to -27
[B]2x - 15 = -27 [/B] <-- This is our algebraic expression
To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D-27&pl=Solve']type 2x - 15 = -27 into the search engine[/URL].

2x plus 4 increased by 15 is 57

2x plus 4 increased by 15 is 57
Take this algebraic expression in parts:
[LIST]
[*]2x plus 4: 2x + 4
[*][I]Increased by[/I] means we add 15 to 2x + 4: 2x + 4 + 15 = 2x + 19
[*]The word [I]is[/I] means an equation, so we set 2x + 19 equal to 57:
[/LIST]
Our final algebraic expression is:
[B]2x + 19 = 57
[/B]
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B19%3D57&pl=Solve']type this equation into our search engine [/URL]and we get
x = [B]19[/B]

3 cartons of eggs for $5 what if the cost of 8 cartons

3 cartons of eggs for $5 what if the cost of 8 cartons
Set up a proportion of cartons of eggs to price where p is the price of 8 cartons:
3/5 = 8/p
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=8&den1=5&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get:
p = [B]13.33[/B]

3 consecutive odd integers such that thrice the middle is 15 more than the sum of the other 2

3 consecutive odd integers such that thrice the middle is 15 more than the sum of the other 2.
[LIST]
[*]Let the first integer be n
[*]The next odd one (middle) is n + 2.
[*]The next odd one is n + 4
[/LIST]
We are given 3(n + 2) = n + n + 4 + 15.
Simplifying, we get:
3n + 6 = 2n + 19
[URL='http://www.mathcelebrity.com/1unk.php?num=3n%2B6%3D2n%2B19&pl=Solve']Plugging that problem[/URL] into our search engine, we get n = 13.
So the next odd integer is 13 + 2 = 15
The next odd integer is 15 + 2 = 17

3 people can build a shed in 8 hours, how long would it take 5 people

3 people can build a shed in 8 hours, how long would it take 5 people
We set up a proportion of people to hours where h is the number of hours for 5 people:
3/8 = 5/h
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=5&den1=8&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']Using our proportion calculator[/URL], we get:
13.3333 hours
But what if the problem asks for minutes? Then we say 8 hours = 60 * 8 = 480 minutes. We set up the proportion where m is the number of minutes:
3/480 = 5/m
In this case, [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=5&den1=480&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']we use our search engine again[/URL] and get:
m = 800

3 to the power of 2 times 3 to the power of x equals 3 to the power of 7

3 to the power of 2 times 3 to the power of x equals 3 to the power of 7.
Write this out:
3^2 * 3^x = 3^7
When we multiply matching coefficients, we add exponents, so we have:
3^(2 + x) = 3^7
Therefore, 2 + x = 7. To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%2Bx%3D7&pl=Solve']type it into our search engine[/URL] and we get:
x = [B]5[/B]

3/10 of a circle equal how many degrees

3/10 of a circle equal how many degrees
A circle is 365 degrees. So [URL='https://www.mathcelebrity.com/fraction.php?frac1=365&frac2=3%2F10&pl=Multiply']we multiply 365 * 3/10 in our search engine[/URL] and get:
219/2
219/2 = [B]109.5 degrees[/B]

3/4 of the students went skiing.there are 24 students in the class. How’s many went?

3/4 of the students went skiing.there are 24 students in the class. How’s many went?
We want 3/4 of 24. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=24&frac2=3/4&pl=Multiply']type 3/4 of 24 into our search engine[/URL] and get:
[B]18 students[/B]

3/5 of workers at a company have enrolled in the 403(b) program. If 24 workers have enrolled in the

3/5 of workers at a company have enrolled in the 403(b) program. If 24 workers have enrolled in the program, how many workers are employed at this company?
We read this as 3/5 of the total workers employed at the company equals 24. Let w be the number of workers. We have the following equation:
3/5w = 24
Run [URL='http://www.mathcelebrity.com/1unk.php?num=3%2F5w%3D24&pl=Solve']3/5w = 24[/URL] through the search engine, we get [B]w = 40[/B].

300 reduced by 5 times my age is 60

300 reduced by 5 times my age is 60
Let my age be a. We have:
5 times my age = 5a
300 reduced by 5 times my age means we subtract 5a from 300:
300 - 5a
The word [I]is[/I] means an equation, so we set 300 - 5a equal to 60 to get our final algebraic expression:
[B]300 - 5a = 60
[/B]
If you have to solve for a, you [URL='https://www.mathcelebrity.com/1unk.php?num=300-5a%3D60&pl=Solve']type this equation into our search engine[/URL] and you get:
a = [B]48[/B]

309 is the same as 93 subtracted from the quantity f times 123

309 is the same as 93 subtracted from the quantity f times 123.
The quantity f times 123:
123f
Subtract 93:
123f - 93
The phrase [I]is the same as[/I] means an equation, so we set 123f - 93 equal to 309
[B]123f - 93 = 309[/B] <-- This is our algebraic expression
If you wish to solve for f, [URL='https://www.mathcelebrity.com/1unk.php?num=123f-93%3D309&pl=Solve']type this equation into the search engine[/URL], and we get f = 3.2683.

339 equals 303 times w, minus 293

339 equals 303 times w, minus 293
Take this algebraic expression in pieces:
303 times w:
303w
Minus 293:
303w - 293
The phrase [I]equals[/I] means we have an equation. We set 303w - 293 = 339
[B]303w - 293 = 339[/B] <-- This is our algebraic expression
To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=303w-293%3D339&pl=Solve']we type this equation into our search engine[/URL] to get:
[B]w = 2.086[/B]

35% of the houses are blue. Write the percent that do not live in blue houses as a decimal and a fra

35% of the houses are blue. Write the percent that do not live in blue houses as a decimal and a fraction in simplest form
The percent that do not live in blue houses is found by:
Not in blue = 100% - 35%
Not in blue = 65%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=65&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Typing 65% in our search engine[/URL], we see that the decimal and fraction is:
[LIST]
[*]65% as a decimal: [B]0.65[/B]
[*]65% as a fraction in simplest form: [B]13/20[/B]
[/LIST]

36% of the pupils in class 2 are boys the remaining 16 are girls how many pupils are in class 2?

36% of the pupils in class 2 are boys the remaining 16 are girls how many pupils are in class 2?
This means 100% - 36% = 64% of the class are girls. And if the class size is s, then we have:
64% of s = 16
Or, written as a decimal:
0.64s = 16
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.64s%3D16&pl=Solve']type it into our search engine[/URL] and we get:
s = [B]25[/B]

38 books into 8 boxes. 6 left. How many books in each box

38 books into 8 boxes. 6 left. How many books in each box
Let the number of books in each box be b. We have the following relation:
8b + 6 = 38
to solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=8b%2B6%3D38&pl=Solve']type it in our search engine[/URL] and we get:
b = [B]4[/B]

3timesanumberdecreasedby3

A necklace chain costs $15. Beads cost $2.50 each. You spend a total of $30 on a necklace and beads before tax. How many beads did you buy in addition to the necklace?
Let the number of beads be b. We're given the following equation:
2.5b + 15 = 30
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5b%2B15%3D30&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]6[/B]

3x less than 2 times the sum of 2x and 1 is equal to the sum of 2 and 5

3x less than 2 times the sum of 2x and 1 is equal to the sum of 2 and 5
This is an algebraic expression. Let's take this algebraic expression in 5 parts:
[LIST=1]
[*]The sum of 2x and 1 means we add 1 to 2x: 2x + 1
[*]2 times the sum of 2x and 1: 2(2x + 1)
[*]3x less than the sum of 2x and 1 means we subtract 3x from 2(2x + 1): 2(2x + 1) - 3x
[*]The sum of 2 and 5 means we add 5 to 2: 2 + 5
[*]Finally, the phrase [I]equal[/I] means an equation, so we set #3 equal to #4
[/LIST]
Our algebraic expression is:
[B]2(2x + 1) - 3x = 2 + 5[/B]
[B][/B]
Now, some problems may ask you to simplify. In this case, we multiply through and group like terms:
4x + 2 - 3x = 7
[B]x + 2 = 7 <-- This is our simplified algebraic expression
[/B]
Now, what if the problem asks you to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B2%3D7&pl=Solve']you type this into our search engine[/URL] and get:
x =[B] 5[/B]

4 machines can complete a job in 6 hours how long will it take 3 machines to complete the same jobs?

4 machines can complete a job in 6 hours how long will it take 3 machines to complete the same jobs?
Set up a proportion of machines to hours where h is the number of hours that 3 machines take:
4/6 = 3/h
[URL='https://www.mathcelebrity.com/prop.php?num1=4&num2=3&den1=6&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get:
h = [B]4.5[/B]

4 teaspons of vegetable oil and 6 teaspoons of vinegar. 20 teaspoons of vegetable oil to how many te

4 teaspons of vegetable oil and 6 teaspoons of vinegar. 20 teaspoons of vegetable oil to how many teaspoons of vinegar?
Set up a proportion where x is the number of teaspoons of vinegar in the second scenario:
4/6 = 20/x
[URL='http://www.mathcelebrity.com/prop.php?num1=4&num2=20&den1=6&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']Plug that expression into the search engine to get[/URL]
[B]x = 30[/B]

4 times 8 to the sixth power

4 times 8 to the sixth power
8 to the 6th power:
8^6
4 times this amount:
4 * 8^6
To evaluate this expression, we [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=4%2A8%5E6&pl=Perform+Order+of+Operations']type it in our search engine[/URL] and we get:
1,048,576

4 times a number added to 8 times a number equals 36

4 times a number added to 8 times a number equals 36
Let [I]a number[/I] be an arbitrary variable, let us call it x.
4 times a number:
4x
8 times a number:
8x
We add these together:
4x + 8x = 12x
We set 12x equal to 36 to get our final algebraic expression of:
[B]12x = 36
[/B]
If the problem asks you to solve for x, you [URL='https://www.mathcelebrity.com/1unk.php?num=12x%3D36&pl=Solve']type this algebraic expression into our search engine[/URL] and get:
x = [B]3[/B]

4 times a number is the same as the number increased by 78

4 times a number is the same as the number increased by 78.
Let's take this algebraic expression in parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]4 times a number is written as 4x
[*]The number increased by 78 means we add 78 to x: x + 78
[*]The phrase [I]the same as[/I] mean an equation, so we set #2 equal to #3
[/LIST]
[B]4x = x + 78[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further, then [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3Dx%2B78&pl=Solve']we type this equation into our search engine [/URL]and get:
x = 26

40% of the days in September were sunny how many days were sunny?

40% of the days in September were sunny how many days were sunny?
September has 30 days. So we [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=40&den1=30&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type 40% of 30 in our search engine[/URL]. We get:
[B]12 days[/B]

400 reduced by 3 times my age is 214

400 reduced by 3 times my age is 214
Let my age be a. We have:
3 times my age:
3a
400 reduced by 3 times my age:
400 - 3a
The word [I]is[/I] means an equation. So we set 400 - 3a equal to 214
400 - 3a = 214
Now if you want to solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D214&pl=Solve']type it in the search engin[/URL]e and we get;
a = [B]62[/B]

41% of the passengers on the plane are men. 36% of them are women and 11% of them are boys. The rema

41% of the passengers on the plane are men. 36% of them are women and 11% of them are boys. The remaining 30 passengers are girls. How many passengers are on the plane?
Add up the percents:
41% + 36% + 11% = 88%
This means that (100% - 88% = 12%) are girls.
So if the total amount of passengers on the plane is p, we write 12% s 0.12, and we have:
0.12p = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=0.12p%3D30&pl=Solve']Type this equation into our search engine[/URL], and we get:
p = [B]250[/B]

450 people attended a concert at the center. the center was 3/4 full. what is the capacity of the mu

450 people attended a concert at the center. the center was 3/4 full. what is the capacity of the music center.
Let the capacity be c. We're given:
3c/4 = 450
To solve this equation, we [URL='https://www.mathcelebrity.com/prop.php?num1=3c&num2=450&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
c = [B]600[/B]

46 people showed up to the party. There were 8 less men than women present. How many men were there?

46 people showed up to the party. There were 8 less men than women present. How many men were there?
Let the number of men be m. Let the number of women be w. We're given two equations:
[LIST=1]
[*]m = w - 8 [I](8 less men than women)[/I]
[*]m + w = 46 [I](46 showed up to the party)[/I]
[/LIST]
Substitute equation (1) into equation (2) for m:
w - 8 + w = 46
To solve for w in this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=w-8%2Bw%3D46&pl=Solve']type in the equation into our search engine [/URL]and we get:
w = 27
To solve for men (m), we substitute w = 27 into equation (1):
m = 27 - 8
m = [B]19[/B]

48 is the difference of Chrissys height and 13 .

48 is the difference of Chrissys height and 13 .
Let Chrissy's height = h.
The difference of the height and 13 is h - 13.
We set this expression equal to 48:
[B]h - 13 = 48
[/B]
Note: To solve this, [URL='http://www.mathcelebrity.com/1unk.php?num=h-13%3D48&pl=Solve']paste this problem into the search engine[/URL].

4800$ salary spent 12% on clothes 20% on house rent how much money is she left with

4800$ salary spent 12% on clothes 20% on house rent how much money is she left with
12% on clothes plus 20% on house rent = 32% total spendings.
If she spent 32%, that means she's left with:
100% - 32% = 68%
So we want 68% of 4800.
We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=68&den1=4800&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type [I]68% of 4800 [/I]into our search engine[/URL] and we get:
[B]3,264[/B]

4subtractedfrom6timesanumberis32

4 subtracted from 6 times a number is 32.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
6 times this number means we multiply by x by 6
6x
4 subtracted from this expression means we subtract 4
6x - 4
The phrase [I]is[/I] means an equation, so we set 6x - 4 equal to 32
[B]6x - 4 = 32
[/B]
If you need to solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=6x-4%3D32&pl=Solve']type it in the search engine here[/URL].

5 added to x is 11

x + 5 = 11 for the algebraic expression.
Plug that into the [URL='http://www.mathcelebrity.com/1unk.php?num=x%2B5%3D11&pl=Solve']search engine[/URL], and solve for x.
x = 6.

5 years ago Kevin was 3 times as old as Tami. Now he is twice as old as she is. How is each now?

5 years ago Kevin was 3 times as old as Tami. Now he is twice as old as she is. How is each now?
Let Kevin's age be k. Let Tami's age be t. We're given the following equations:
[LIST=1]
[*]k - 5 = 3(t - 5)
[*]k = 2t
[/LIST]
Plug equation (2) into equation (1) for k:
2t - 5 = 3(t - 5)
We p[URL='https://www.mathcelebrity.com/1unk.php?num=2t-5%3D3%28t-5%29&pl=Solve']lug this equation into our search engine[/URL] and we get:
t = [B]10. Tami's age[/B]
Now plug t = 10 into equation (2) to solve for k:
k = 2(10)
k =[B] 20. Kevin's age[/B]

5/8 Of a class are boys. what fraction of the class are girls

5/8 Of a class are boys. what fraction of the class are girls?
The total class equals 1. Since 5/8 are boys, we subtract 5/8 from 1:
1 - 5/8
But we can write 1 as 8/8. So we have
8/8 - 5/8
[URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F8&frac2=5%2F8&pl=Subtract']Type this fraction operation into our search engine[/URL] and we get:
[B]3/8[/B] are girls

5000 union members of a financially troubled company accepted a 17% pay cut. The company announced t

5000 union members of a financially troubled company accepted a 17% pay cut. The company announced that this would save them approximately $108 million annually. Based on this information, calculate the average annual pay of a single union member
Let the full salary of the union members be s. Since 17% is 0.17, We're given:
0.17s = 108000000
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.17s%3D108000000&pl=Solve']type it in our search engine[/URL] and we get:
s = 635,294,117.65
Calculate the average annual pay of a single union member:
Average Pay = Total Pay / Number of Union Members
Average Pay = 635,294,117.65 / 5000
Average Pay = [B]127,058.82[/B]

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $885.50. How many kids and how many adults were there?
Assumptions:
[LIST]
[*]Let the number of adults be a
[*]Let the number of kids be k
[/LIST]
Given with assumptions:
[LIST=1]
[*]a + k = 508
[*]2a + 1.25k = 885.50 (since cost = price * quantity)
[/LIST]
Rearrange equation (1) by subtracting c from each side to isolate a:
[LIST=1]
[*]a = 508 - k
[*]2a + 1.25k = 885.50
[/LIST]
Substitute equation (1) into equation (2):
2(508 - k) + 1.25k = 885.50
Multiply through:
1016 - 2k + 1.25k = 885.50
1016 - 0.75k = 885.50
To solve for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=1016-0.75k%3D885.50&pl=Solve']type this equation into our search engine[/URL] and we get:
k = [B]174[/B]
Now, to solve for a, we substitute k = 174 into equation 1 above:
a = 508 - 174
a = [B]334[/B]

55 foot tall tree casts a shadow that is 32 feet long, a nearby woman is 5.5 feet tall. What is the

55 foot tall tree casts a shadow that is 32 feet long, a nearby woman is 5.5 feet tall. What is the length of shadow she will cast?
Set up a proportion of height to shadow length where s is the shadow length of the woman:
55/32 = 5.5/s
[URL='https://www.mathcelebrity.com/prop.php?num1=55&num2=5.5&den1=32&den2=s&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
s = [B]3.2[/B]

59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving.

59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving.
The phrase [I]the sum of[/I] means we add Donnie's savings of d to 16:
d + 16
The phrase [I]is[/I] means an equation, so we set d + 16 equal to 59
d + 16 = 59 <-- [B]This is our algebraic expression[/B]
Now, if the problem asks you to solve for d, then you[URL='https://www.mathcelebrity.com/1unk.php?num=d%2B16%3D59&pl=Solve'] type the algebraic expression into our search engine to get[/URL]:
d = [B]43[/B]

5y^0=15x for y

5y^0=15x for y
y^0 = 1, so we have:
5(1) = 15x
5 = 15x
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=5%3D15x&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]1/3[/B]

6 books cost 9.24. How much is 1 book

6 books cost 9.24. How much is 1 book
Set up a proportion of cost to books where x is the cost for 1 book:
9.24/6 = x/1
To solve this proportion for x, we [URL='https://www.mathcelebrity.com/prop.php?num1=9.24&num2=x&den1=6&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
x = [B]1.54[/B]

6 times a number multiplied by 3 all divided by 4

6 times a number multiplied by 3 all divided by 4
Take this algebraic expression in parts:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]6 times a number: 6x
[*]Multiplied by 3: 3(6x) = 18x
[*]All divided by 4: 18x/4
[/LIST]
We can simplify this:
We type 18/4 into our search engine, simplify, and we get 9/2. So our answer is:
[B]9x/2[/B]

6 times a number, x, is at least 22.

6 times a number, x, is at least 22.
6 times a number x:
6x
The phrase [I]is at least[/I] means greater than or equal to. So we have an inequality:
[B]6x >= 22[/B] <-- This is our algebraic expression
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6x%3E%3D22&pl=Show+Interval+Notation']To solve this for x, paste this into the search engine[/URL] and we get:
[B]x >= 3.666667[/B]

6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number

6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number
We've got two algebraic expressions here. Let's take it in parts:
Term 1:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The reciprocal is 1/x
Multiply this by 6: 6/x
Term 2:
Reciprocal of 7: 1/7
2 times this: 2/7
We set these terms equal to each other:
6/x = 2/7
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=2&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get:
[B]x = 21[/B]

6 times the reciprocal of a number equals 3 times the reciprocal of 7 .

6 times the reciprocal of a number equals 3 times the reciprocal of 7 .
This is an algebraic expression. Let's take it in parts:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of a number x means we divide 1 over x:
1/x
6 times the reciprocal means we multiply 6 by 1/x:
6/x
The reciprocal of 7 means we divide 1/7
1/7
3 times the reciprocal means we multiply 1/7 by 3:
3/7
Now, the phrase [I]equals[/I] mean an equation, so we set 6/x = 3/7
[B]6/x = 3/7[/B] <-- This is our algebraic expression
If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=3&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']we type this proportion in our search engine[/URL] and get:
x = 14

6 times the sum of a number and 3 is equal to 42. What is this number?

6 times the sum of a number and 3 is equal to 42. What is this number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The sum of a number and 3 means we add 3 to x:
x + 3
6 times the sum:
6(x + 3)
The word [I]is[/I] means an equation, so we set 6(x + 3) equal to 42 to get our [I]algebraic expression[/I] of:
[B]6(x + 3) = 42[/B]
[B][/B]
If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/1unk.php?num=6%28x%2B3%29%3D42&pl=Solve']you type this equation into our search engine[/URL] and you get:
x = [B]4[/B]

60 percent of a number minus 17 is -65

60 percent of a number minus 17 is -65
Using our [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=60&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percent to decimal calculator[/URL], we see that 60% is 0.6, so we have:
0.6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So 60% of a number is:
0.6x
Minus 17:
0.6x - 17
The word [I]is[/I] means an equation, so we set 0.6x - 17 equal to -65 to get our algebraic expression of:
[B]0.6x - 17 = -65[/B]
[B][/B]
If you want to solve for x in this equation, you [URL='https://www.mathcelebrity.com/1unk.php?num=0.6x-17%3D-65&pl=Solve']type it in our search engine and you get[/URL]:
[B]x = -80[/B]

64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44.

64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44.
The phrase [I]difference between[/I] means we subtract 44 from a:
a - 44
The phrase [I]64 is[/I] means an equation, so we set a - 44 equal to 64
[B]a - 44 = 64 <-- This is our algebraic expression
[/B]
If you want to solve for a, then we [URL='https://www.mathcelebrity.com/1unk.php?num=a-44%3D64&pl=Solve']type this expression into our search engine[/URL] and get:
[B]a = 108[/B]

64 is 4 times the difference between Sarah’s age a, and 44.Assume Sarah is older than 44

64 is 4 times the difference between Sarah’s age a, and 44.Assume Sarah is older than 44
Difference between Sarah's age (a) and 44 (Assuming Sarah is older than 44):
a - 44
4 times the difference:
4(a - 44)
The word [I]is[/I] means equal to, so we set 4(a - 44) equal to 64 to get our algebraic expression:
[B]4(a - 44) = 64[/B]
If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=4%28a-44%29%3D64&pl=Solve']type this equation into our search engine[/URL] and we get:
a = [B]60[/B]

7 and 105 are successive terms in a geometric sequence. what is the term following 105?

7 and 105 are successive terms in a geometric sequence. what is the term following 105?
Geometric sequences are set up such that the next term in the sequence equals the prior term multiplied by a constant. Therefore, we express the relationship in the following equation:
7k = 105 where k is the constant
[URL='https://www.mathcelebrity.com/1unk.php?num=7k%3D105&pl=Solve']Type this equation into our search engine[/URL] and we get:
k = 15
The next term in the geometric sequence after 105 is found as follows:
105*15 = [B]1,575[/B]

7 black shirts 5 white shirts 10 gray shirts one is chosen at random, what is the probability that i

7 black shirts 5 white shirts 10 gray shirts one is chosen at random, what is the probability that it is not gray
[U]Find the total shirts:[/U]
Total shirts = Black Shirts + White Shirts + Gray Shirts
Total shirts = 7 + 5 + 10
Total shirts = 22
[U]Calculate the probability of choosing a gray shirt:[/U]
P(Gray) = Number of Gray shirts / Total Shirts
P(Gray) = 10/22
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=10%2F22&frac2=3%2F8&pl=Simplify']type in 10/22 into our search engine, choose simplify[/URL], and we get:
P(Gray) = [B]5/11[/B]

7 multiplied by the quantity 7 take away 6

7 multiplied by the quantity 7 take away 6
Take this algebraic expression in pieces:
[LIST]
[*]7 take away 6: 7 - 6
[*]7 multiplied by the quantity: [B]7(7 - 6)[/B]
[/LIST]
This is our algebraic expression.
If you need to evaluate this expression, we [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=7%287-6%29&pl=Perform+Order+of+Operations']type it in the search engine[/URL] and we get;
[B]7[/B]

7/4 yards represents 4/5 of the full length of rope. Find the length of the entire jump rope.

7/4 yards represents 4/5 of the full length of rope. Find the length of the entire jump rope.
Let the entire jump rope length be l. We're given the proportion:
4l/5 = 7/4
We type this in our search engine and our [URL='https://www.mathcelebrity.com/prop.php?num1=4l&num2=7&den1=5&den2=4&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] solves for l to get:
l = [B]2.1875 yards[/B]

75% of a ship’s cargo was destroyed by an on-board fire. The captain of the ship sold the remaining

75% of a ship’s cargo was destroyed by an on-board fire. The captain of the ship sold the remaining cargo, which was slightly damaged, for 25% of its real value and received $1400. What was the value of the cargo before the fire? (Do not include the $ sign or commas in the answer)
So 25% of the cargo is left.
This was sold at 25% of value.
Let the starting value be s:
We have 0.25 * 0.25 * s = 1400
0.0625s = 1400
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.0625s%3D1400&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]22400[/B]

75% of x is 25 dollars and 99 cents

75% of x is 25 dollars and 99 cents
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=75&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Since 75%[/URL] is 0.75 as a decimal, we rewrite this as an algebraic expression:
0.75x = 25.99
If we want to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.75x%3D25.99&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]34.65[/B]

8 bricklayers can build a wall in 10 days. How long would it take 5 bricklayers to build?

8 bricklayers can build a wall in 10 days. How long would it take 5 bricklayers to build?
Set up a proportion of bricklayers to building time where t is the amount of time it takes 5 bricklayers to build a wall:
8/10 = 5/t
To solve this proportion for t, we [URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=5&den1=10&den2=t&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
t = [B]6.25 days[/B]

8 more than the product of x and 2 equals 4

8 more than the product of x and 2 equals 4
The product of x and 2:
2x
8 more than this, means we add 8:
2x + 8
Set this equal to 4:
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B8%3D4&pl=Solve']2x + 8 = 4[/URL] <-- Algebraic expression
to solve for x, type this into the search engine and we get [B]x = -2[/B].

8 sweets are shared among 4 pupils. how many does each pupil get

8 sweets divided by 4 pupils = 2 sweets per pupil.
We can also write this as a proportion:
8 sweets x sweets
---------- = ------------
4 pupils 1 pupil
Express this as 8/4 = x/1.
[URL='http://www.mathcelebrity.com/prop.php?num1=8&num2=x&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Enter that into the search engine[/URL]
x = 2

8 times the difference of a number and 2 is the same as 3 times the sum of the number and 3. What is

8 times the difference of a number and 2 is the same as 3 times the sum of the number and 3. What is the number?
Let the number be n. We're given two expressions:
[LIST=1]
[*]8(n - 2) [I]difference means we subtract[/I]
[*]3(n + 3) [I]sum means we add[/I]
[/LIST]
The phrase [I]is the same as[/I] mean an equation. So we set the first expression equal to the second expression:
8(n - 2) = 3(n + 3)
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=8%28n-2%29%3D3%28n%2B3%29&pl=Solve']type it in our search engine[/URL] and we see that:
n =[B] 5[/B]

8 years from now a girls age will be 5 times her present age whats is the girls age now

8 years from now a girls age will be 5 times her present age whats is the girls age now.
Let the girl's age now be a. We're given:
a + 8 = 5a
[URL='https://www.mathcelebrity.com/1unk.php?num=a%2B8%3D5a&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]a = 2[/B]

84% as a fraction in simplest form

84% as a fraction in simplest form
Enter [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=84&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']84% as a fraction into our search engine[/URL] and we get:
[B]21/25[/B]

9 divided by the sum of x and 4 is equal to 6 divided by x minus 4

9 divided by the sum of x and 4 is equal to 6 divided by x minus 4.
Build our two algebraic expressions first:
9 divided by the sum of x and 4
9/(x + 4)
6 divided by x minus 4
6/(x - 4)
The phrase [I]is equal to[/I] means and equation, so we set the algebraic expressions equal to each other:
[B]9/(x + 4) = 6/(x - 4) <-- This is our algebraic expression[/B]
[B][/B]
If the problem asks you to solve for x, we cross multiply:
9(x - 4) = 6(x + 4)
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%28x-4%29%3D6%28x%2B4%29&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]20[/B]

9 is one-third of a number x

9 is one-third of a number x
A number x can be written as x
x
one-third of a number x means we multiply x by 1/3:
x/3
The phrase [I]is[/I] means an equation, so we set 9 equal to x/3 to get our final algebraic expression of:
[B]x/3 = 9[/B]
If the problem asks you to solve for x, you [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=9&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type this algebraic expression into our search engine[/URL] and you get:
[B]x = 27[/B]

9 less than 5 times a number is 3 more than 2x

9 less than 5 times a number is 3 more than 2x
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
5 times a number means we multiply x by 5:
5x
9 less than 5x means we subtract 9 from 5x:
5x - 9
3 more than 2x means we add 3 to 2x:
2x + 3
The word [I]is[/I] means an equation, so we set 5x - 9 equal to 2x + 3:
[B]5x - 9 = 2x + 3 <-- This is our algebraic expression[/B]
[B][/B]
If you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-9%3D2x%2B3&pl=Solve']type this equation into the search engine[/URL], and we get:
x = [B]4[/B]

9 times a number is that number minus 3

9 times a number is that number minus 3
Let [I]a number[/I] be an arbitrary variable, let's call it x. We're given:
9 times a number is 9x
The number minus 3 is x - 3
The word [I]is[/I] means an equation, so we set 9x equal to x - 3 to get our [I]algebraic expression[/I]:
[B]9x = x - 3[/B]
To solve for x, we type this equation into our search engine and we get:
x = [B]-0.375 or -3/8[/B]

A $480 TV was put on sale for 30% off. It didn't sell, so the price was lowered an additional percen

A $480 TV was put on sale for 30% off. It didn't sell, so the price was lowered an additional percent off the sale price, making the new sale price $285.60. What was the second percent discount that was given?
Let the second discount be d. We're given:
480 * (1 - 0.3)(1 - d) = 285.60
480(0.7)(1 - d) = 285.60
336(1 - d) = 285.60
336 - 336d = 285.60
[URL='https://www.mathcelebrity.com/1unk.php?num=336-336d%3D285.60&pl=Solve']Type this equation into our search engine[/URL] to solve for d and we get:
d = [B]0.15 or 15%[/B]

A $675 stereo receiver loses value at a rate of about $18 per month The equation y = 675 - 18x repre

A $675 stereo receiver loses value at a rate of about $18 per month The equation y = 675 - 18x represents the value of the receiver after x months. Identify and interpret the x- and y-intercepts. Explain how you can use the intercepts to help you graph the equation
y = 675 - 18x
The y-intercept is found when x is 0:
y = 675 - 18(0)
y = 675 - 0
y = 675
The x-intercept is found when y is 0:
0 = 675 - 18x
[URL='https://www.mathcelebrity.com/1unk.php?num=675-18x%3D0&pl=Solve']Typing this equation into our search engine[/URL], we get:
x = 37.5

A 1.5 inch tall preying mantis will sometimes hold its ground and attempt to fight a person who is 6

A 1.5 inch tall preying mantis will sometimes hold its ground and attempt to fight a person who is 6 feet tall. If a person who is 6 feet tall is engaged in a battle with an animal that was proportionally as tall as the person is to the preying mantis, how tall would the animal be?
In terms of inches, [URL='https://www.mathcelebrity.com/linearcon.php?quant=6&pl=Calculate&type=foot']6 feet = 72 inches[/URL]
Set up a proportion of height of smaller creature to larger creature where h is the heigh of the animal
1.5/72 = 72/h
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=1.5&num2=72&den1=72&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
h = 3456 inches
In terms of feet, we have [URL='https://www.mathcelebrity.com/linearcon.php?quant=3456&pl=Calculate&type=inch']3456 inches[/URL] = [B]288 feet[/B]

A 10 ounce serving of energy drink contains about 190 mg of caffeine approximately how much caffeine

A 10 ounce serving of energy drink contains about 190 mg of caffeine approximately how much caffeine is in a 25 ounce of energy drink?
Set up a proportion of caffeine to ounces where c is the amount of caffeine in a 25 ounce drink:
190/10 = c/25
[URL='https://www.mathcelebrity.com/prop.php?num1=190&num2=c&den1=10&den2=25&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL] and we get:
c = [B]475[/B]

A 12-ounce bottle of shampoo lasts Enrique 16 weeks. How long would you expect an 18-ounce bottle of

A 12-ounce bottle of shampoo lasts Enrique 16 weeks. How long would you expect an 18-ounce bottle of the same brand to last him?
Set up a proportion of ounces to weeks were w is the amount of weeks an 18-ounce bottle will last:
12/16 = 18/w
We [URL='https://www.mathcelebrity.com/prop.php?num1=12&num2=18&den1=16&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion in our search engine to solve for w[/URL] and we get:
w = [B]24[/B]

A 124-inch length of ribbon is to be cut into three pieces. The longest piece is to be 36 inches lo

A 124-inch length of ribbon is to be cut into three pieces. The longest piece is to be 36 inches longer than the shortest piece, and the third piece is to be half the length of the longest piece. Find the length of each piece of ribbon.
[LIST]
[*]Let the longest piece be l.
[*]The shortest piece is s = l - 36
[*]The third medium piece m = 0.5l
[/LIST]
We know s + m + l = 124. Now substitute for s and m
(l - 36) + 0.5l + l = 124
Combine like terms:
2.5l - 36 = 124
Type [URL='http://www.mathcelebrity.com/1unk.php?num=2.5l-36%3D124&pl=Solve']2.5l - 36 = 124 into our search engine[/URL], we get l = [B]64[/B]
Shortest piece s = 64 - 36 = [B]28[/B]
Medium piece m = 0.5(64) = [B]32[/B]

A 16 pound roast will feed 24 people. If the largest roast you can buy is 12 pounds. How many people

A 16 pound roast will feed 24 people. If the largest roast you can buy is 12 pounds. How many people can you feed?
Set up a proportion of roast pounds to people fed, where p is the number of people fed on a 12 pound roast:
16/24 = 12/p
[URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=12&den1=24&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Run this through our proportion calculator[/URL] by typing 16/24 = 12/p into our search engine.
We get [B]p = 18[/B].
A 12 pound roast will feed 18 people.

A 20 oz. bottle of Pepsi costs $1.60 in 2010 and $1.85 in 2014. What is the percent of increase? Rou

A 20 oz. bottle of Pepsi costs $1.60 in 2010 and $1.85 in 2014. What is the percent of increase? Round to the nearest percent if necessary.
We [URL='https://www.mathcelebrity.com/markup.php?p1=1.60&m=&p2=1.85&pl=Calculate']type 1.60 to 1.85 percent increase in our search engine[/URL] and we get:
[B]15.63% percent increase[/B]

A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an ho

A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey?
[U]Set up the relationship of still water speed and downstream speed[/U]
Speed down stream = Speed in still water + speed of the current
Speed down stream = x+2
Therefore:
Speed upstream =x - 2
Since distance = rate * time, we rearrange to get time = Distance/rate:
15/(x+ 2) + 15 /(x- 2) = 3
Multiply each side by 1/3 and we get:
5/(x + 2) + 5/(x - 2) = 1
Using a common denominator of (x + 2)(x - 2), we get:
5(x - 2)/(x + 2)(x - 2) + 5(x + 2)/(x + 2)(x - 2)
(5x - 10 + 5x + 10)/5(x - 2)/(x + 2)(x - 2)
10x = (x+2)(x-2)
We multiply through on the right side to get:
10x = x^2 - 4
Subtract 10x from each side:
x^2 - 10x - 4 = 0
This is a quadratic equation. To solve it, [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2-10x-4%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine[/URL] and we get:
Speed of the boat in still water =X=5 +- sq. Root of 29 kmph
We only want the positive solution:
x = 5 + sqrt(29)
x = 10.38
[U]Calculate time for upstream journey:[/U]
Time for upstream journey = 15/(10.38 - 2)
Time for upstream journey = 15/(8.38)
Time for upstream journey = [B]1.79[/B]
[U]Calculate time for downstream journey:[/U]
Time for downstream journey = 15/(10.38 + 2)
Time for downstream journey = 15/(12.38)
Time for downstream journey = [B]1.21[/B]

A 7-foot piece of cotton cloth costs $3.36. What is the price per inch?

A 7-foot piece of cotton cloth costs $3.36. What is the price per inch?
Using [URL='https://www.mathcelebrity.com/linearcon.php?quant=7&pl=Calculate&type=foot']our length converter[/URL], we see that:
7 feet = 84 inches
So $3.36 for 84 inches. We [URL='https://www.mathcelebrity.com/perc.php?num=3.36&den=84&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']divide $3.36 by 84[/URL] to get the cost per inch:
$3.36/84 = [B]0.04 per inch[/B]

A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every

A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag?
Let the red marbles be r
Let the black marbles be b.
A 19 to 1 red to black is written as:
r = 19b
We're also given:
b + r = 120
Substitute r = 19b into this equation and we get:
b + 19b = 120
Combine like terms:
20b = 120
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=20b%3D120&pl=Solve']we type it in our search engine [/URL]and we get:
b = 6
Since r = 19b, we substitute b = 6 into this equation to solve for r:
r = 19(6)
r = [B]114[/B]

A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles. You select one marble at random f

A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles. You select one marble at random from the bag. What is P(blue)
P(blue) = Number of blue marbles / Total Marbles
P(blue) = 5 / (5 + 6 + 4)
P(blue) = 5/15
We can reduce this. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F15&frac2=3%2F8&pl=Simplify']type in 5/15 into our search engine, choose simplify[/URL], and we get:
P(blue) = [B]1/3[/B]

A bag contains 8 marbles of different colors. How many ways unique ways or orders can you select 3 m

A bag contains 8 marbles of different colors. How many ways unique ways or orders can you select 3 marbles?
We want the combinations formula, 8 choose 3, or 8C3.
[URL='https://www.mathcelebrity.com/permutation.php?num=8&den=3&pl=Combinations']Type 8 C 3 into our search engine and we get:[/URL]
[B]56 unique ways[/B]

A bag contains tiles, 3 tiles are red. 6 tiles are green, and 3 tiles are blue. A tile will be rando

A bag contains tiles, 3 tiles are red. 6 tiles are green, and 3 tiles are blue. A tile will be randomly selected from the bag . What is the probability that the tile selected will be green
P(green) = Number of green tiles / Total Tiles
P(green) = 6 / (3 + 6 + 3)
P(green) = 6 / 12
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F12&frac2=3%2F8&pl=Simplify']type in 6/12 into our search engine, pick simplify[/URL], and we get:
P(green) = [B]1/2 or 0.5[/B]

A bag has 3 red, 5 blue, and 2 yellow pieces of candy. What is the theoretical probability of drawin

A bag has 3 red, 5 blue, and 2 yellow pieces of candy. What is the theoretical probability of drawing a blue piece of candy
P(Blue) = Blue Candies / Total Candies
P(Blue) = 5 / (3 + 5 + 2)
P(Blue) = 5 / 10
We can [URL='https://www.mathcelebrity.com/search.php?q=5%2F10&x=0&y=0']simplify this using our GCF calculator[/URL] and we get:
P(Blue) = [B]1/2[/B]

A bag of quarters and nickels is worth $8.30. There are two less than three times as many quarters a

A bag of quarters and nickels is worth $8.30. There are two less than three times as many quarters as nickels. How many of the coins must be quarters?
Assumptions and givens:
[LIST]
[*]Let the number of quarters be q
[*]Let the number of nickels be n
[/LIST]
We have two equations:
[LIST=1]
[*]0.05n + 0.25q = 8.30
[*]n = 3q - 2 [I](Two less than Three times)[/I]
[/LIST]
Plug in equation (2) into equation (1) for q to solve this system of equations:
0.05(3q - 2) + 0.25q = 8.30
To solve this equation for q, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.05%283q-2%29%2B0.25q%3D8.30&pl=Solve']type it in our search engine[/URL] and we get:
q = [B]21[/B]

A bag of rice says to mix 3 cups of rice with 2 cups of water. How much water would be needed to mix

A bag of rice says to mix 3 cups of rice with 2 cups of water. How much water would be needed to mix with 2 cups of rice?
Set up a proportion of cups of rice to water where w is the amount of water needed for 2 cups of rice:
3/2 = 2/w
To solve this proportion for w, we [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=2&den1=2&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
w = [B]1.33333[/B]

A bakery offers a sale price of $3.50 for 4 muffins. What is the price per dozen?

A bakery offers a sale price of $3.50 for 4 muffins. What is the price per dozen?
1 dozen = 12 muffins
What this problem is really asking, $3.50 for 4 muffins. Let p be the price for 12 muffins (1 dozen). Set up a proportion of cost to muffins.
3.50/4 = p/12
Using our math engine, we [URL='https://www.mathcelebrity.com/prop.php?num1=3.50&num2=p&den1=4&den2=12&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search box[/URL] and get:
p = [B]10.5 muffins
[MEDIA=youtube]ccY7yDkKvzs[/MEDIA][/B]

A bamboo tree grew 3 inches per day. How many days will it take the tree to grow 144 inches? Choose

A bamboo tree grew 3 inches per day. How many days will it take the tree to grow 144 inches? Choose the correct equation to represent this situation.
Let the number of days be d. We have the equation:
3d = 144
To solve this equation for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=3d%3D144&pl=Solve']type it in our search engine[/URL] and we get:
d = [B]48[/B]

A bank charges a service fee of $7.50 per month for a checking account. A bank account has $85.00. I

A bank charges a service fee of $7.50 per month for a checking account. A bank account has $85.00. If no money is deposited or withdrawn except the service charge, how many months until the account balance is negative?
Let m be the number of months. Our balance is denoted by B(m):
B(m) = 85 - 7.5m
The question asks when B(m) is less than 0. So we set up an inequality:
85 - 7.5m < 0
To solve this inequality for m, [URL='https://www.mathcelebrity.com/1unk.php?num=85-7.5m%3C0&pl=Solve']we type it in our search engine[/URL] and we get:
m > 11.3333
We round up to the next whole integer and get [B]m = 12[/B]

A baseball player gets 3 hits in the first 15 games of the season. If he continues hitting at the sa

A baseball player gets 3 hits in the first 15 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 45 games?
We set up a proportion of hits to games where h is the number of hits the player gets in 45 games:
3/15 = h/45
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=h&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']Enter this into our search engine[/URL], and we get [B]h = 9[/B].

a baseball player has 9 hits in his first 60 at bats. how many consecutive hits would he need to bri

a baseball player has 9 hits in his first 60 at bats. how many consecutive hits would he need to bring his average up to 0.400?
Let the amount of consecutive hits needed be h. We have:
hits / at bats = Batting Average
Plugging in our numbers, we get:
(9 + h)/60 = 0.400
Cross multiply:
9 + h = 60 * 0.4
9 + h = 24
To solve this equation for h, [URL='https://www.mathcelebrity.com/1unk.php?num=9%2Bh%3D24&pl=Solve']we type it in our search engine[/URL] and we get:
h = [B]15[/B]

A baseball team won 40% of its first 30 games. The team then won 65% of its next 60 games. Approxima

A baseball team won 40% of its first 30 games. The team then won 65% of its next 60 games. Approximately what percent of the games did the team win?
Using our percentage calculators, we type the following statements into our search engine and get:
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=45&den1=30&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']45% of 30[/URL] = 13.5
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=65&den1=60&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']65% of 60[/URL] = 39
For a total of 52.5 games won
The team played 30 + 60 = 90 games. So we want to know the pecent:
[URL='https://www.mathcelebrity.com/perc.php?num=52&den=90&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']52/90[/URL] = [B]57.78%[/B]

A bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The ave

A bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $80. How many bicycles must the store sell each month to break even?
Profit = Revenue - Cost
Let the number of bikes be b.
Revenue = 80b
Cost = 60b + 1500
Break even is when profit equals 0, which means revenue equals cost. Set them equal to each other:
60b + 1500 = 80b
We [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B1500%3D80b&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]75[/B]

A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The a

A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The average selling price of each bicycle is $95. How many bicycles must the store sell each month to break even?
Let the number of bikes be b.
Set up our cost function, where it costs $45 per bike to produce
C(b) = 45b
Set up our revenue function, where we earn $95 per sale for each bike:
R(b) = 95b
Set up our profit function, which is how much we keep after a sale:
P(b) = R(b) - C(b)
P(b) = 95b - 45b
P(b) = 50b
The problem wants to know how many bikes we need to sell to break-even. Note: break-even means profit equals operating cost, which in this case, is $2,750. So we set our profit function of 50b equal to $2,750
50b = 2750
[URL='https://www.mathcelebrity.com/1unk.php?num=50b%3D2750&pl=Solve']We type this equation into our search engine[/URL], and we get:
b = [B]55[/B]

A bicycle wheel is one meter around. If the spikes are 4 centimeters apart, how many spokes are on t

A bicycle wheel is one meter around. If the spikes are 4 centimeters apart, how many spokes are on the wheel altogether?
1 meter = 100 cm per our [URL='https://www.mathcelebrity.com/linearcon.php?quant=1&pl=Calculate&type=meter']conversions calculator[/URL]
100 cm for the whole circle / 4 cm for each spike = [B]25 spikes[/B]

A bowl contains 45 oranges. If ? of the oranges are bad; how many are good?

A bowl contains 45 oranges. If ? of the oranges are bad; how many are good?
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=2%2F3&pl=Subtract']fraction operator calculator[/URL], we see that:
1 - 2/3 = 1/3 of the oranges are good.
We want 1/3 of 45. [URL='https://www.mathcelebrity.com/fraction.php?frac1=45&frac2=1/3&pl=Multiply']Typing this expression into our search engine[/URL], we get:
[B]15 good oranges[/B]

A box contains 5 plain pencils and 3 pens. A second box contains 2 color pencils and 2 crayons . One

A box contains 5 plain pencils and 3 pens. A second box contains 2 color pencils and 2 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected
[U]Calculate the probability of a plain pencil in the first box:[/U]
P(plain pencil in the first box) = Total Pencils / Total Objects
P(plain pencil in the first box) = 5 pencils / (5 pencils + 3 pens)
P(plain pencil in the first box) = 5/8
[U]Calculate the probability of a color pencil in the first box:[/U]
P(color in the second box) = Total Pencils / Total Objects
P(color in the second box) = 2 pencils / (2 pencils + 2 crayons)
P(color in the second box) = 2/4
We can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F4&frac2=3%2F8&pl=Simplify']Type 2/4 into our search engine[/URL] and we get 1/2
Now the problem asks for the probability that a plain pencil from the first box and a color pencil from the second box are selected.
Since each event is independent, we multiply them together to get our answer:
P(plain pencil in the first box, color in the second box) = P(plain pencil in the first box) * P(color in the second box)
P(plain pencil in the first box, color in the second box) = 5/8 * 1/2
P(plain pencil in the first box, color in the second box) = [B]5/16[/B]

A box had x pencils. Then 6 pencils were removed from the box. The box now has 54 pencils.

A box had x pencils. Then 6 pencils were removed from the box. The box now has 54 pencils.
Removed means we subtract from the total. So Our equation is:
x - 6 = 54
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-6%3D54&pl=Solve']type it in our search engine [/URL]and we get:
x = [B]60[/B]

A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find th

A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find the present age of each?
Let the boy's age be b and his brother's age be c. We're given two equations:
[LIST=1]
[*]b = c + 10
[*]b + 4 = 2(c + 4)
[/LIST]
Substitute equation (1) into equation (2):
(c + 10) + 4 = 2(c + 4)
Simplify by multiplying the right side through and grouping like terms:
c + 14 = 2c + 8
[URL='https://www.mathcelebrity.com/1unk.php?num=c%2B14%3D2c%2B8&pl=Solve']Type this equation into our search engine[/URL] and we get:
c = [B]6[/B]
Now plug c = 6 into equation (1):
b = 6 + 10
b = [B]16[/B]

A boy is 6 years older than his sister. In 3 years time he will be twice her age. What are their pre

A boy is 6 years older than his sister. In 3 years time he will be twice her age. What are their present ages?
Let b be the boy's age and s be his sister's age. We're given two equations:
[LIST=1]
[*]b = s + 6
[*]b + 3 = 2(s + 3)
[/LIST]
Plug in (1) to (2):
(s + 6) + 3 = 2(s + 3)
s + 9 = 2s + 6
[URL='https://www.mathcelebrity.com/1unk.php?num=s%2B9%3D2s%2B6&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]s = 3[/B]
We plug s = 3 into Equation (1) to get the boy's age (b):
b = 3 + 6
[B]b = 9[/B]

a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that

a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that the middle piece is 6inches longer than the shortest piece and the shortest piece is 9 inches shorter than the longest price. how long should the three pieces be?
Let the longest piece be l. The middle piece be m. And the short piece be s. We have 2 equations in terms of the shortest piece:
[LIST=1]
[*]l = s + 9 (Since the shortest piece is 9 inches shorter, this means the longest piece is 9 inches longer)
[*]m = s + 6
[*]s + m + l = 57
[/LIST]
We substitute equations (1) and (2) into equation (3):
s + (s + 6) + (s + 9) = 57
Group like terms:
(1 + 1 + 1)s + (6 + 9) = 57
3s + 15 = 57
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3s%2B15%3D57&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]14
[/B]
[U]Plug s = 14 into equation 2 to solve for m:[/U]
m = 14 + 6
m = [B]20
[/B]
[U]Plug s = 14 into equation 1 to solve for l:[/U]
l = 14 + 9
l = [B]23
[/B]
Check our work for equation 3:
14 + 20 + 23 ? 57
57 = 57 <-- checks out
[B][/B]

A bus is carrying 135 passengers, which is 3/4 of the capacity of the bus. What is the capacity of t

A bus is carrying 135 passengers, which is 3/4 of the capacity of the bus. What is the capacity of the bus
Let the capacity of the bus be c. We're given:
3c/4 = 135
To solve for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=3c&num2=135&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type this equation into our search engine [/URL]and we get:
c = [B]180[/B]

A bus ride cost 1.50. A 30 day pass cost $24. Write an inequallity to show that the 30 day pass is t

A bus ride cost 1.50. A 30 day pass cost $24. Write an inequallity to show that the 30 day pass is the better deal
Let the number of days be d. We have the inequality below where we show when the day to day cost is greater than the monthly pass:
1.5d > 24
To solve this inequality for d, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.5d%3E24&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]d > 16[/B]

A cab company charges $5 per cab ride, plus an additional $1 per mile driven , How long is a cab rid

A cab company charges $5 per cab ride, plus an additional $1 per mile driven , How long is a cab ride that costs $13?
Let the number of miles driven be m. Our cost function C(m) is:
C(m) = Cost per mile * m + cab cost
C(m) = 1m + 5
The problem asks for m when C(m) = 13:
1m + 5 = 13
To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=1m%2B5%3D13&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]8[/B]

A cab company charges $5 per cab ride, plus an additional $3 per mile driven. How long is a cab ride

A cab company charges $5 per cab ride, plus an additional $3 per mile driven. How long is a cab ride that costs $17?
Let m be the number of miles driven. We setup the cost equation C(m):
C(m) = Cost per mile driven * miles driven + ride cost
C(m) = 3m + 5
The questions asks for m when C(m) is 17:
3m + 5 = 17
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%2B5%3D17&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]4[/B]

A cable company charges $75 for installation plus $20 per month. Another cable company offers free i

A cable company charges $75 for installation plus $20 per month. Another cable company offers free installation but charges $35 per month. For how many months of cable service would the total cost from either company be the same
[U]Set ups the cost function for the first cable company C(m) where m is the number of months:[/U]
C(m) = cost per month * m + installation fee
C(m) = 20m + 75
[U]Set ups the cost function for the second cable company C(m) where m is the number of months:[/U]
C(m) = cost per month * m + installation fee
C(m) = 35m
The problem asks for m when both C(m) functions are equal. So we set both C(m) functions equal and solve for m:
20m + 75 = 35m
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=20m%2B75%3D35m&pl=Solve']type this equation into our search engine[/URL] and we get:
m = [B]5[/B]

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drin

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 14 minutes?
Set up a proportion of gallons of water over minutes where g is the number of gallons the camel can drink in 14 minutes:
15/10 = g/14
[URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=g&den1=10&den2=14&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
[B]g = 21[/B]

A car is traveling 60 km per hour. How many hours will it take for the car to reach a point that is

A car is traveling 60 km per hour. How many hours will it take for the car to reach a point that is 180 km away?
Rate * Time = Distance so we have t for time as:
60t = 180
To solve this equation for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=60t%3D180&pl=Solve']type it in the search engine[/URL] and we get:
t = [B]3[/B]

a car is worth 24000 and it depreciates 3000 a year how long till it costs 9000

a car is worth 24000 and it depreciates 3000 a year how long till it costs 9000
Let y be the number of years. We want to know y when:
24000 - 3000y = 9000
Typing [URL='https://www.mathcelebrity.com/1unk.php?num=24000-3000y%3D9000&pl=Solve']this equation into our search engine[/URL], we get:
y = [B]5[/B]

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the mon

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the month. If he is aiming to earn a minimum of $3200 a month, what is the possible value of sales that will enable this?
to start, we have:
[LIST]
[*]Let the salesman's monthly sales be s.
[*]With a 10% discount as a decimal of 0.1
[*]The phrase [I]a minimum[/I] also means [I]at least[/I] or [I]greater than or equal to[/I]. This tells us we want an inequality
[*]We want 10% times s + 800 per month is greater than or equal to 3200
[/LIST]
We want the inequality:
0.1s + 800 >= 3200
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.1s%2B800%3E%3D3200&pl=Solve']type this inequality into our search engine[/URL] and we get:
[B]s >= 24000[/B]

a car was bought for $24300 and sold at a loss of $2290. Find the selling price.

a car was bought for $24300 and sold at a loss of $2290. Find the selling price.
A loss means the car was sold for less than the buying price. Let the selling price be S. we have:
24300 - S = 2290
[URL='https://www.mathcelebrity.com/1unk.php?num=24300-s%3D2290&pl=Solve']Typing this equation into our search engine[/URL], we get:
s = [B]22,010[/B]

A car who’s original value was $25600 decreases in value by $90 per month. How Long will it take bef

A car who’s original value was $25600 decreases in value by $90 per month. How Long will it take before the cars value falls below $15000
Let m be the number of months.We have our Book Value B(m) given by:
B(m) = 25600 - 90m
We want to know when the Book value is less than 15,000. So we have an inequality:
25600 - 90m < 15000
Typing [URL='https://www.mathcelebrity.com/1unk.php?num=25600-90m%3C15000&pl=Solve']this inequality into our search engine and solving for m[/URL], we get:
[B]m > 117.78 or m 118 months[/B]

a card is drawn at random from a standard 52 card deck. find the probability that the card is not a

a card is drawn at random from a standard 52 card deck. find the probability that the card is not a king.
There are 4 kings in a standard 52 card deck. To not get a king, we'd have 52 - 4 = 48 possible cards.
The probability of not drawing a King is 48/52.
But we can simplify this. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=48%2F52&frac2=3%2F8&pl=Simplify']type the fraction 48/52 into our search engine[/URL], and get:
[B]12/13[/B]

A card is drawn from a standard deck of 52 cards. What is the probability of drawing an ace or a 6

A card is drawn from a standard deck of 52 cards. What is the probability of drawing an ace or a 6?
There are 4 Ace's in a standard 52 card deck. There are 4 6's as well.
So we have 4 + 4 = 8 possible cards out of 52:
8/52
To simplify, [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F52&frac2=3%2F8&pl=Simplify']we type this into our search engine[/URL] and we get:
[B]2/13[/B]

a carnival charges $6 admission and $2.50 per ride. You have $50 to spend at the carnival. Which of

a carnival charges $6 admission and $2.50 per ride. You have $50 to spend at the carnival. Which of the following inequalities represents the situation if r is the number of rides?
We set up our inequality using less than or equal to, since our cash is capped at $50. We use S for our :
Cost per ride * r + Admission <= 50
Plugging in our numbers, we get:
2.50r + 6 <= 50
[B][/B]
Now, if the problem asks you to put this in terms of r, then [URL='https://www.mathcelebrity.com/1unk.php?num=2.50r%2B6%3C%3D50&pl=Solve']we plug this inequality into our search engine[/URL] and we get:
r <= 17.6
Since we cannot do fractional rides, we round down to 17:
[B]r <= 17[/B]

A carnival charges a $15 admission price. Each game at the carnival costs $4. How many games would a

A carnival charges a $15 admission price. Each game at the carnival costs $4. How many games would a person have to play to spend at least $40?
Let g be the number of games. The Spend function S(g) is:
S(g) = Cost per game * number of games + admission price
S(g) = 4g + 15
The problem asks for g when S(g) is at least 40. At least is an inequality using the >= sign:
4g + 15 >= 40
To solve this inequality for g, we type it in our search engine and we get:
g >= 6.25
Since you can't play a partial game, we round up and get:
[B]g >= 7[/B]

A carpenter wants to cut a 45 inch board into two pieces such that the longer piece will be 7 inches

A carpenter wants to cut a 45 inch board into two pieces such that the longer piece will be 7 inches longer than the shorter. How long should each piece be
Let the shorter piece of board length be s. Then the larger piece is:
[LIST]
[*]l = s + 7
[/LIST]
And we know that:
Shorter Piece + Longer Piece = 25
Substituting our values above, we have:
s + s + 7 = 45
to solve this equation for s, we type it in our search engine and we get:
s = [B]19[/B]
Plugging this into our equation for l above means that:
l = 19 + 7
l =[B] 26[/B]

A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge

A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge of 25¢ per square foot for any footage that exceeds 180 sq ft and $1.30 per step for any carpeting on a staircase. A customers cleaning bill was $253.95. This included the cleaning of a staircase with 14 steps. In addition to the staircase, how many square feet of carpet did the customer have cleaned?
Calculate the cost of the staircase cleaning.
Staircase cost = $1.30 * steps
Staircase cost = $1.30 * 14
Staircase cost = $18.20
Subtract this from the cost of the total cleaning bill of $253.95. We do this to isolate the cost of the carpet.
Carpet cost = $253.95 - $18.20
Carpet cost = $235.75
Now, the remaining carpet cost can be written as:
75 + $0.25(s - 180) = $235.75 <-- were s is the total square foot of carpet cleaned
Multiply through and simplify:
75 + 0.25s - 45 = $235.75
Combine like terms:
0.25s + 30 = 235.75
[URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B30%3D235.75&pl=Solve']Type this equation into our search engine[/URL] to solve for s, and we get:
s = [B]823[/B]

A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How

A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How many of each type of bill does the cashier have?
Let a be the amount of $10 bills and b be the amount of $20 bills. We're given two equations:
[LIST=1]
[*]a + b = 44
[*]10a + 20b = 730
[/LIST]
We rearrange equation 1 in terms of a. We subtract b from each side and we get:
[LIST=1]
[*]a = 44 - b
[*]10a + 20b = 730
[/LIST]
Now we substitute equation (1) for a into equation (2):
10(44 - b) + 20b = 730
Multiply through to remove the parentheses:
440 - 10b + 20b = 730
Group like terms:
440 + 10b = 730
Now, to solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=440%2B10b%3D730&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]29
[/B]
To get a, we take b = 29 and substitute it into equation (1) above:
a = 44 - 29
a = [B]15
[/B]
So we have [B]15 ten-dollar bills[/B] and [B]29 twenty-dollar bills[/B]

A certain Illness is spreading at a rate of 10% per hour. How long will it take to spread to 1,200 p

A certain Illness is spreading at a rate of 10% per hour. How long will it take to spread to 1,200 people if 3 people initially exposes? Round to the nearest hour.
Let h be the number of hours. We have the equation:
3 * (1.1)^h = 1,200
Divide each side by 3:
1.1^h = 400
[URL='https://www.mathcelebrity.com/natlog.php?num=1.1%5Eh%3D400&pl=Calculate']Type this equation into our search engine [/URL]to solve for h:
h = 62.86
To the nearest hour, we round up and get [B]h = 63[/B]

A certain race is a distance of 26 furlongs. How far is the race in (a) miles? (b) yards?

A certain race is a distance of 26 furlongs. How far is the race in (a) miles? (b) yards?
[URL='https://www.mathcelebrity.com/linearcon.php?quant=26&pl=Calculate&type=furlong']We type in [I]26 furlongs[/I] into our search engine[/URL] and we get:
[LIST]
[*][B]3.25 miles[/B]
[*][B]5,720 yards[/B]
[/LIST]

A certain species of fish costs $3.19 each. You can spend at most $35. How many of this type of f

A certain species of fish costs $3.19 each. You can spend at most $35. How many of this type of fish can you buy for your aquarium?
Let the number of fish be f. We have the following inequality where "at most" means less than or equal to:
3.19f <= 35
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3.19f%3C%3D35&pl=Show+Interval+Notation']Typing this inequality into our search engine[/URL], we get:
f <= 10.917
Since we need a whole number of fish, we can buy a maximum of [B]10 fish[/B].

A checking account is set up with an initial balance of $2400 and $200 are removed from the account

A checking account is set up with an initial balance of $2400 and $200 are removed from the account each month for rent right and equation who solution is the number of months and it takes for the account balance to reach 1000
200 is removed, so we subtract. Let m be the number of months. We want the following equation:
[B]2400 - 200m = 1000
[/B]
Now, we want to solve this equation for m. So [URL='https://www.mathcelebrity.com/1unk.php?num=2400-200m%3D1000&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]7[/B]

A class has 35 boys and girls. There are 7 more girls than boys. Find the number of girls and boys i

A class has 35 boys and girls. There are 7 more girls than boys. Find the number of girls and boys in the class
Let the number of boys be b and the number of girls be g. We're given two equations:
[LIST=1]
[*]b + g = 35
[*]g = b + 7 (7 more girls means we add 7 to the boys)
[/LIST]
To solve for b, we substitute equation (2) into equation (1) for g:
b + b + 7 = 35
To solve for b, we type this equation into our search engine and we get:
b = [B]14[/B]
Now, to solve for g, we plug b = 14 into equation (2) above:
g = 14 + 7
g = [B]21[/B]

A classroom had x students. Then 9 of them went home. There are now 27 students in the classroom.

A classroom had x students. Then 9 of them went home. There are now 27 students in the classroom.
Take this one piece at a time:
[LIST]
[*]We start with x students
[*]9 of them went home. This means we have 9 less students. So we subtract 9 from x: x - 9
[*]The phrase [I]there are now[/I] means an equation, so we set x - 9 equal to 27
[/LIST]
x - 9 = 27
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-9%3D27&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]36[/B]

a collection of 7 pencils, every week 3 more pencils are added How many weeks will it take to have 3

a collection of 7 pencils, every week 3 more pencils are added How many weeks will it take to have 30 pencils?
Set up a function, P(w), where w is the number of weeks, and P(w) is the total amount of pencils after w weeks. We have:
P(w) = 3w + 7
We want to know what w is when P(w) = 30
3w + 7 = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=3w%2B7%3D30&pl=Solve']Typing this equation into our search engine[/URL], we get:
w = 7.6667
We round up to the nearest integer, so we get [B]w = 8[/B]

A collection of nickels and dime has a total value of $8.50. How many coins are there if there are 3

A collection of nickels and dime has a total value of $8.50. How many coins are there if there are 3 times as many nickels as dimes.
Let n be the number of nickels. Let d be the number of dimes. We're give two equations:
[LIST=1]
[*]n = 3d
[*]0.1d + 0.05n = 8.50
[/LIST]
Plug equation (1) into equation (2) for n:
0.1d + 0.05(3d) = 8.50
Multiply through:
0.1d + 0.15d = 8.50
[URL='https://www.mathcelebrity.com/1unk.php?num=0.1d%2B0.15d%3D8.50&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]d = 34[/B]
Now, we take d = 34, and plug it back into equation (1) to solve for n:
n = 3(34)
[B]n = 102[/B]

A college student earns $21 per day delivering advertising brochures door-to-door, plus 50 cents for

A college student earns $21 per day delivering advertising brochures door-to-door, plus 50 cents for each person he interviews. How many people did he interview on a day when he earned $61.50
Let each person interviewed be p. We have an earnings equation E(p):
E(p) = 0.5p + 21
The problems asks for p when E(p) = 61.50
0.5p + 21 = 61.50
To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.5p%2B21%3D61.50&pl=Solve']type this equation in our search engine[/URL] and we get:
p = [B]81[/B]

A company charges $7 for a T-Shirt and ships and order for $22. A school principal ordered a number

A company charges $7 for a T-Shirt and ships and order for $22. A school principal ordered a number of T-shirts for the school store. The total cost of the order was $1,520. Which equation can be used to find the number one f shirts ordered?
Set up the cost equation C(f) where f is the number of shirts:
C(f) = Cost per shirt * f + Shipping
We're given C(f) = 1520, Shipping = 22, and cost per shirt is 7, so we have:
[B]7f + 22 = 1520
[/B]
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=7f%2B22%3D1520&pl=Solve']type this equation in our search engine[/URL] and we get:
f = [B]214[/B]

a company has revenue given by R(x)=500x dollars and total cost given by C(x)=48,000 100x dollars, w

a company has revenue given by R(x)=500x dollars and total cost given by C(x)=48,000 + 100x dollars, where x is the number of units produced and sold. How many units will give a profit
Profit P(x) is given by:
R(x) - C(x)
So we have:
P(x) = 500x - (100x + 48,000)
P(x) = 500x - 100x - 48,000
P(x) = 400x - 48,000
A profit is found when P(x) > 0, so we have:
400x - 48000 > 0
To solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=400x-48000%3E0&pl=Solve']we type it into our search engine [/URL]and we get:
[B]x > 120[/B]

A company specializes in personalized team uniforms. It costs the company $15 to make each uniform a

A company specializes in personalized team uniforms. It costs the company $15 to make each uniform along with their fixed costs at $640. The company plans to sell each uniform for $55.
[U]The cost function for "u" uniforms C(u) is given by:[/U]
C(u) = Cost per uniform * u + Fixed Costs
[B]C(u) = 15u + 640[/B]
Build the revenue function R(u) where u is the number of uniforms:
R(u) = Sale Price per uniform * u
[B]R(u) = 55u[/B]
Calculate break even function:
Break even is where Revenue equals cost
C(u) = R(u)
15u + 640 = 55u
To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=15u%2B640%3D55u&pl=Solve']type this equation into our search engine[/URL] and we get:
u = [B]16
So we break even selling 16 uniforms[/B]

A company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each l

A company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each lamp, and the selling price is $150 per lamp.
Set up the Cost Equation C(l) where l is the price of each lamp:
C(l) = Variable Cost x l + Fixed Cost
C(l) = 90l + 1800
Determine the revenue function R(l)
R(l) = 150l
Determine the profit function P(l)
Profit = Revenue - Cost
P(l) = 150l - (90l + 1800)
P(l) = 150l - 90l - 1800
[B]P(l) = 60l - 1800[/B]
Determine the break even point:
Breakeven --> R(l) = C(l)
150l = 90l + 1800
[URL='https://www.mathcelebrity.com/1unk.php?num=150l%3D90l%2B1800&pl=Solve']Type this into the search engine[/URL], and we get [B]l = 30[/B]

A computer was on sale. The original cost of the computer was $900. It’s on sale for 5/6 the price.

A computer was on sale. The original cost of the computer was $900. It’s on sale for 5/6 the price. How much is the computer now?
We want 5/6 of 900. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=900&frac2=5/6&pl=Multiply']type this in our search engine[/URL] and we get:
[B]750[/B]

A construction company can remove 2/3 tons of dirt from a construction site each hour. How long wil

A construction company can remove 2/3 tons of dirt from a construction site each hour. How long will it take them to remove 30 tons of dirt from the site?
Let h be the number of hours. We have the following equation:
2/3h = 30
Multiply each side by 3:
2(3)h/3 = 30 * 3
Cancel the 3 on the left side:
2h = 90
[URL='https://www.mathcelebrity.com/1unk.php?num=2h%3D90&pl=Solve']Type 2h = 90 into the search engine[/URL], we get [B]h = 45[/B].

A construction worker can lift 220 lb, while an architect can only lift 40 lb. The construction work

A construction worker can lift 220 lb, while an architect can only lift 40 lb. The construction worker can lift how many times what the architect can lift?
[URL='https://www.mathcelebrity.com/perc.php?num=220&den=40&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']We divide 220 by 40 to get the multiplier:[/URL]
220/40 = [B]5.5 times[/B]

A copy machine makes 44 copies per minute. How many copies does it make in 5 minutes and 45 seconds

A copy machine makes 44 copies per minute. How many copies does it make in 5 minutes and 45 seconds
Set up a proportion of copies to minutes where c is the number of copies for 5 minutes and 45 seconds.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=45%2F60&frac2=3%2F8&pl=Simplify']Since 45 seconds[/URL] is:
45/60 = 3/4 of a minute, we have:
5 minutes and 45 seconds = 5.75 minutes
44/1 = c/5.75
To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=44&num2=c&den1=1&den2=5.75&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
c = [B]253[/B]

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixe

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixed costs are $110,000 per month and the feed sells for $132 per ton, how many tons should be sold each month to have a monthly profit of $560,000?
[U]Set up the cost function C(t) where t is the number of tons of cattle feed:[/U]
C(t) = Variable Cost * t + Fixed Costs
C(t) = 84t + 110000
[U]Set up the revenue function R(t) where t is the number of tons of cattle feed:[/U]
R(t) = Sale Price * t
R(t) = 132t
[U]Set up the profit function P(t) where t is the number of tons of cattle feed:[/U]
P(t) = R(t) - C(t)
P(t) = 132t - (84t + 110000)
P(t) = 132t - 84t - 110000
P(t) = 48t - 110000
[U]The question asks for how many tons (t) need to be sold each month to have a monthly profit of 560,000. So we set P(t) = 560000:[/U]
48t - 110000 = 560000
[U]To solve for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=48t-110000%3D560000&pl=Solve']type this equation into our search engine[/URL] and we get:[/U]
t =[B] 13,958.33
If the problem asks for whole numbers, we round up one ton to get 13,959[/B]

A cubical storage box has edges that are 2 feet 4 inches long. What is the volume of the storage box

A cubical storage box has edges that are 2 feet 4 inches long. What is the volume of the storage box?
Since 1 foot = 12 inches, we have:
2 feet 4 inches = 2(12) + 4
2 feet 4 inches = 24 + 4
2 feet 4 inches = 28 inches
We type [URL='https://www.mathcelebrity.com/cube.php?num=28&pl=Side&type=side&show_All=1']cube side = 28[/URL] into our search engine to get:
V = [B]21952 cubic inches[/B]

A daily pass costs $62. A season ski pass costs $450. The skier would have to rent skis with eithe

A daily pass costs $62. A season ski pass costs $450. The skier would have to rent skis with either pass for $30 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
Let d be the number of days the skier attends.
Calculate the daily cost:
Daily Total Cost = Daily Cost + Rental Cost
Daily Total Cost = 62d + 30d
Daily Total Cost = 92d
Calculate Season Cost:
Season Total Cost = Season Fee + Rental Cost
Season Total Cost = 450 + 30d
Set the daily total cost and season cost equal to each other:
450 + 30d = 92d
[URL='https://www.mathcelebrity.com/1unk.php?num=450%2B30d%3D92d&pl=Solve']Typing this equation into the search engine[/URL], we get d = 7.258.
We round up to the next full day of [B]8[/B].
Now check our work:
Daily Total Cost for 8 days = 92(8) = 736
Season Cost for 8 days = 30(8) + 450 = 240 + 450 = 710.
Therefore, the skier needs to go at least [B]8 days[/B] to make the season cost less than the daily cot.

A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at

A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at a profit of 4 per pig. His total profit was $56. How many pigs did he originally buy?
Let p be the purchase price of pigs. We're given:
[LIST]
[*]Farmer originally bought [I]p [/I]pigs for 232 which is our cost C.
[*]5 of them died, so he has p - 5 left
[*]He sells 4(p - 5) pigs for a revenue amount R
[*]Since profit is Revenue - Cost, which equals 56, we have:
[/LIST]
Calculate Profit
P = R - C
Plug in our numbers:
4(p - 5) - 232 = 56
4p - 20 - 232 = 56
To solve for p, [URL='https://www.mathcelebrity.com/1unk.php?num=4p-20-232%3D56&pl=Solve']we type this equation into our search engine[/URL] and we get:
p = [B]77[/B]

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. F

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. Find the numbers.
[U]The phrase [I]a number[/I] means an arbitrary variable[/U]
A first number is written as x
A second number is written as y
[U]Twice a second number means we multiply y by 2:[/U]
2y
[U]A first number plus twice a second number:[/U]
x + 2y
[U]A first number plus twice a second number is 10 means we set x + 2y equal to 10:[/U]
x + 2y = 10
[U]Twice the first number means we multiply x by 2:[/U]
2x
[U]Twice the first number plus the second:[/U]
2x + y
[U]Twice the first number plus the second totals 35 means we set 2x + y equal to 35:[/U]
2x + y = 35
Therefore, we have a system of two equations:
[LIST=1]
[*]x + 2y = 10
[*]2x + y = 35
[/LIST]
Since we have an easy multiple of 2 for the x variable, we can solve this by multiply the first equation by -2:
[LIST=1]
[*]-2x - 4y = -20
[*]2x + y = 35
[/LIST]
Because the x variables are opposites, we can add both equations together:
(-2 + 2)x + (-4 + 1)y = -20 + 35
The x terms cancel, so we have:
-3y = 15
To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D15&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]-5
[/B]
Now we substitute this y = -5 into equation 2:
2x - 5 = 35
To solve this equation for x, we[URL='https://www.mathcelebrity.com/1unk.php?num=2x-5%3D35&pl=Solve'] type it in our search engine[/URL] and we get:
x = [B]20[/B]

A first number plus twice a second number is 14. Twice the first number plus the second totals 40. F

A first number plus twice a second number is 14. Twice the first number plus the second totals 40. Find the numbers.
[B][U]Givens and assumptions:[/U][/B]
[LIST]
[*]Let the first number be x.
[*]Let the second number be y.
[*]Twice means multiply by 2
[*]The phrases [I]is[/I] and [I]totals[/I] mean equal to
[/LIST]
We're given two equations:
[LIST=1]
[*]x + 2y = 14
[*]2x + y = 40
[/LIST]
To solve this system, we can take a shortcut, and multiply the top equation by -2 to get our new system:
[LIST=1]
[*]-2x - 4y = -28
[*]2x + y = 40
[/LIST]
Now add both equations together
(-2 _ 2)x (-4 + 1)y = -28 + 40
-3y = 12
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D12&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]-4
[/B]
We substitute this back into equation 1 for y = -4:
x + 2(-4) = 14
x - 8 = 14
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-8%3D14&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]22[/B]

A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Fi

A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Find the numbers.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x + 2y = 6
[*]2x + y = 15
[/LIST]
Multiply the first equation by -2:
[LIST=1]
[*]-2x - 4y = -12
[*]2x + y = 15
[/LIST]
Now add them
-2x + 2x - 4y + y = -12 + 15
-3y = 3
Divide each side by -3:
y = 3/-3
y =[B] -1[/B]
Plug this back into equation 1:
x + 2(-1) = 6
x - 2 = 6
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-2%3D6&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]8[/B]

A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will

A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will its dimensions be?
A flower bed has a rectangle shape, so the area is:
A = lw
We are given l = w + 3
Plugging in our numbers given to us, we have:
108 = w(w + 3)
w^2 + 3w = 108
Subtract 108 from each side:
w^2 + 3w - 108 = 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B3w-108%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get:
w = (9, -12)
Since length cannot be negative, w = 9.
And l = 9 + 3 --> l = 12
So we have [B](l, w) = (12, 9)[/B]
Checking our work, we have:
A = (12)9
A = 108 <-- Match!

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from sel

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day?
Let the number of drinks be d. Let the number of salads be s. We're given two equations:
[LIST=1]
[*]2d + 6.50s = 836.50
[*]d + s = 209
[/LIST]
We can use substitution to solve this system of equations quickly. The question asks for the number of salads (s). Therefore, we want all expressions in terms of s. Rearrange Equation 2 by subtracting s from both sides:
d + s - s = 209 - s
Cancel the s's, we get:
d = 209 - s
So we have the following system of equations:
[LIST=1]
[*]2d + 6.50s = 836.50
[*]d = 209 - s
[/LIST]
Substitute equation (2) into equation (1) for d:
2(209 - s) + 6.50s = 836.50
Multiply through to remove the parentheses:
418 - 2s + 6.50s = 836.50
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=418-2s%2B6.50s%3D836.50&pl=Solve']type it into our search engine and we get[/URL]:
s = [B]93[/B]

a football team won 3 more games than it lost.the team played 11 games.how many did it win?

a football team won 3 more games than it lost.the team played 11 games.how many did it win?
Let wins be w. Let losses be l. We're given two equations:
[LIST=1]
[*]w = l + 3
[*]l + w = 11
[/LIST]
Plug equation (1) into equation (2) to solve for l:
l + (l + 3) = 11
Group like terms:
2l + 3 = 11
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B3%3D11&pl=Solve']Typing this equation into our search engine[/URL], we get:
l = 4
To solve for w, we plug in l = 4 above into equation (1):
w = 4 + 3
w = [B]7[/B]

A garden table and a bench cost $977 combined. The garden

A garden table and a bench cost $977 combined. The garden table costs $77 more than the bench. What is the cost of the bench?
Let the garden table cost be g and the bench cost be b. We're given
[LIST=1]
[*]b + g = 977
[*]g = b + 77 <-- The phrase [I]more than[/I] means we add
[/LIST]
Substitute (2) into (1):
b + (b + 77) = 977
Combine like terms:
2b + 77 = 977
[URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B77%3D977&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]b = $450[/B]

A girl is three years older than her brother. If their combined age is 35 years, how old is each

A girl is three years older than her brother. If their combined age is 35 years, how old is each
Let the girl's age be g. Let the boy's age be b. We're given two equations:
[LIST=1]
[*]g = b + 3 ([I]Older means we add)[/I]
[*]b + g = 35
[/LIST]
Now plug in equation (1) into equation (2) for g:
b + b + 3 = 35
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2Bb%2B3%3D35&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]16
[/B]
Now, to solve for g, we plug in b = 16 that we just solved for into equation (1):
g = 16 + 3
g = [B]19[/B]

A girl makes 12 foul shots for every eight that she misses how many shots did you make if she shot 1

A girl makes 12 foul shots for every eight that she misses how many shots did you make if she shot 125 foul shots
This means she makes 12/20
We want to know x shots, if 12/20 = x/125.
[URL='http://www.mathcelebrity.com/prop.php?num1=12&num2=x&den1=20&den2=125&propsign=%3D&pl=Calculate+missing+proportion+value']Enter this proportion into the search engine[/URL] to get [B]x = 75[/B]

A grocer is selling oranges at 3 for $2. How much would it cost to buy a dozen oranges?

A grocer is selling oranges at 3 for $2. How much would it cost to buy a dozen oranges?
Set up a proportion of oranges per cost where c is the cost of a dozen oranges:
3/2 = 12/c <-- A dozen equals 12
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=12&den1=2&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
c = [B]8[/B]

A group of campers have 250 pounds of food. They plan to eat 12 pounds a day. How many days will it

A group of campers have 250 pounds of food. They plan to eat 12 pounds a day. How many days will it take them to eat the food. Write your answer in a linear equation.
Let the number of days be d. We have the following equation:
12d = 250
To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=12d%3D250&pl=Solve']type this equation in our search engine[/URL] and we get:
d = [B]20.833[/B]

A high school graduating class is made up of 440 students. There are 168 more girls than boys. How m

A high school graduating class is made up of 440 students. There are 168 more girls than boys. How many boys are in the class?
Let b be the number of boys and g be the number of girls. We're given 2 equations:
[LIST=1]
[*]b + g = 440
[*]g = b + 168
[/LIST]
Substitute (2) into (1)
b + (b + 168) = 440
Combine like terms:
2b + 168 = 440
[URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B168%3D440&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]b = 136[/B]

a horse and a saddle cost $5,000. if the horse cost 4 times as much as the saddle, what was the cost

a horse and a saddle cost $5,000. if the horse cost 4 times as much as the saddle, what was the cost of each?
Let the cost of the horse be h, and the cost of the saddle be s. We're given:
[LIST=1]
[*]h + s = 5000
[*]h = 4s
[/LIST]
Substitute equation (2) into equation (1):
4s + s = 5000
[URL='https://www.mathcelebrity.com/1unk.php?num=4s%2Bs%3D5000&pl=Solve']Type this equation into the search engine[/URL], we get:
[B]s = 1,000[/B]
Substitute s = 1000 into equation (2):
h = 4(1000)
[B]h = 4,000[/B]

A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus

A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus $15 per hour. How long is a job for which companies will charge the same amount?
Set up the cost function C(h) where h is the number of hours.
Company 1:
C(h) = 12h + 376
Company 2:
C(h) = 15h + 280
To see when the companies charge the same amount, set both C(h) functions equal to each other.
12h + 376 = 15h + 280
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B376%3D15h%2B280&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]32[/B]

A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus

A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus $15 per hour. How long is a job for which both companies will charge the same amount?
[U]Set up the cost function for the first company C(h) where h is the number of hours:[/U]
C(h) = Hourly Rate * h + flat rate
C(h) = 12h + 376
[U]Set up the cost function for the first company C(h) where h is the number of hours:[/U]
C(h) = Hourly Rate * h + flat rate
C(h) = 15h + 280
The problem asks how many hours will it take for both companies to charge the same. So we set the cost functions equal to each other:
12h + 376 = 15h + 280
Plugging this equation [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B376%3D15h%2B280&pl=Solve']into our search engine and solving for h[/URL], we get:
h = [B]32[/B]

a jar contains a $5 note, two $10 notes, a $20 note and a $50 note. if 2 notes are taken out by rand

a jar contains a $5 note, two $10 notes, a $20 note and a $50 note. if 2 notes are taken out by random, find the probability that their sum is $15
To get a sum of $15, we'd need to pull the $5 and the $10.
Since both events are indepdenent, we have:
P($5 or 10) or P(whatever is not pulled in the first pull)
First Pull: 2/4 (We can pull either a $10 or a $5, so 2 choices out of 4 bills)
Second Pull: 1/3 <-- since there are only 3 bills and 1 bill to pull
Each pull is independent, so we multiply:
2/4 * 1/3 = 2/12
We can simply this, so [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F12&frac2=3%2F8&pl=Simplify']we type this fraction in our search engine[/URL] and we get:
[B]1/6[/B]

A jet left Nairobi and flew east at an average speed of 231 mph. A passenger plane left four hours l

A jet left Nairobi and flew east at an average speed of 231 mph. A passenger plane left four hours later and flew in the same direction but with an average speed of 385 mph. How long did the jet fly before the passenger plane caught up?
Jet distance = 231t
Passenger plane distance = 385(t - 4)
385(t - 4) = 231t
385t - 1540 = 231t
Subtract 231t from each side
154t = 1540
[URL='https://www.mathcelebrity.com/1unk.php?num=154t%3D1540&pl=Solve']Type 154t = 1540[/URL] into the search engine, we get [B]t = 10.
[/B]
Check our work:
Jet distance = 231(10) = 2,310
Passenger plane distance = 385(10 - 4) = 385 * 6 = 2,310

a large fry has 120 more calories than a small. 5 large fries is the same amount of calories as 7 sm

a large fry has 120 more calories than a small. 5 large fries is the same amount of calories as 7 small. How many calories does each size fry have?
Let the number of calories in large fries be l. Let the number of calories in small fries be s. We're given two equations:
[LIST=1]
[*]l = s + 120
[*]5l = 7s
[/LIST]
Substitute equation (1) into equation (2):
5(s + 120) = 7s
[URL='https://www.mathcelebrity.com/1unk.php?num=5%28s%2B120%29%3D7s&pl=Solve']Type this equation into the search engine[/URL] and we get:
s = [B]300[/B]
Substitute s = 300 into equation (1):
l = 300 + 120
l = [B]420[/B]

a lighthouse blinks every 12 minutes. A second lighthouse blinks every 10 minutes if they both blink

a lighthouse blinks every 12 minutes. A second lighthouse blinks every 10 minutes if they both blink at 8:10 P.M at what time will they next blink together
We want the least common multiple of (10, 12). This will be the next time each number times a multiple equals the same number.
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=10&num2=12&num3=&pl=GCF+and+LCM']Typing in LCM 10,12 into our search engine[/URL], we get:
60
So if we start at 8:10, and 60 minutes later is when both lighthouses blink. 60 minutes equals 1 hour.
So we add 1 hour to 8:10, we have [B]9:10[/B]

A lighthouse blinks every 12 minutes.A second lighthouse blinks every 10 minutes.If they both blink

A lighthouse blinks every 12 minutes.A second lighthouse blinks every 10 minutes.If they both blink at 8:10 P.M., at what time will they next blink together?
We want to know the least common multiple, so that 12 and 10 intervals meet again.[URL='https://www.mathcelebrity.com/gcflcm.php?num1=10&num2=12&num3=&pl=GCF+and+LCM'] We type in LCM(10,12) into our search engine[/URL] and we get 60.
60 minutes is 1 hour, so we add this to 8:10 to get [B]9:10[/B]

A line has a slope of 1/2 and a run of 50. Find the rise of the line.

A line has a slope of 1/2 and a run of 50. Find the rise of the line.
Slope = Rise/Run
We're given a run of 50, so let the rise be r. We have:
r/50 = 1/2
To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=r&num2=1&den1=50&den2=2&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
r = [B]25[/B]

A line joins A (1, 3) to B (5, 8). (a) (i) Find the midpoint of AB.

A line joins A (1, 3) to B (5, 8). (a) (i) Find the midpoint of AB.
We type in (1,3),(5,8) to our search engine. We [URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=3&slope=+2%2F5&xtwo=5&ytwo=8&pl=You+entered+2+points']choose our midpoint of 2 points calculator,[/URL] and we get:
[B](3, 11/2)[/B]

a lion can run 72 feet in one second how far can the lion run in one minute

a lion can run 72 feet in one second how far can the lion run in one minute?
Using our [URL='https://www.mathcelebrity.com/timecon.php?quant=1&pl=Calculate&type=minute']time conversions calculator by typing [I]1 minute[/I] into our search engine[/URL], we see:
1 minute = 60 seconds
So 72 feet per second * 60 seconds / minute = [B]4,320 feet / minute[/B]

A loaf of bread has 35 slices. Ann eats 8 slices, Betty eats 6 slices, Carl eats 5, and Derrick eats

A loaf of bread has 35 slices. Ann eats 8 slices, Betty eats 6 slices, Carl eats 5, and Derrick eats 9 slices. What fraction of the loaf is left?
[U]Calculate total slices eaten:[/U]
Slices eaten = Ann + Betty + Carl + Derrick
Slices eaten = 8 + 6 + 5 + 9
Slices eaten = 28
[U]Calculate remaining slices:[/U]
Remaining slices = Slices in loaf - Slices Eaten
Remaining slices = 35 - 28
Remaining slices = 7
[U]Calculate fraction of the loaf left:[/U]
Fraction left = Remaining Slices / Slices in Loaf
Fraction left = 7/35
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=7%2F35&frac2=3%2F8&pl=Simplify']type 7/35 into our search engine[/URL], choose simplify, and we get:
Fraction left = [B]1/5[/B]

A local bank charges 19 per month plus 3 cents per check. The credit union charges7 per month plus

A local bank charges 19 per month plus 3 cents per check. The credit union charges7 per month plus 7 cents per check. How many checks should be written each month to make the credit union a better deal?
Set up the cost function B(c) for the local bank where c is the number of checks:
B(c) = 0.03c + 19
Set up the cost function B(c) for the credit union where c is the number of checks:
B(c) = 0.07c + 7
We want to find out when:
0.07c + 7 < 0.03c + 19
[URL='https://www.mathcelebrity.com/1unk.php?num=0.07c%2B7%3C0.03c%2B19&pl=Solve']Typing this inequality into our search engine[/URL], we get:
c < 300

A local sports centre charges $8 per visit. For an annual membership fee of$45, the cost per visit i

A local sports centre charges $8 per visit. For an annual membership fee of$45, the cost per visit is only $5.50. What is the least number of visits needed in a year in order for the membership to be a better deal?
Set up the cost for the visitors plan C(v) where v is the number of visits:
C(v) = 8v
Set up the cost for the membership plan C(v) where v is the number of visits:
C(v) = 5v + 45
The problem asks for v where:
5v + 45 < 8v
[URL='https://www.mathcelebrity.com/1unk.php?num=5v%2B45%3C8v&pl=Solve']Type this inequality into our search engine[/URL] and get:
v > 15
This means, the least number of visits is 1 more which is [B]16[/B]

A machine shop employee earned $642 last week. She worked 40hours at her regular rate and 9 hours at

A machine shop employee earned $642 last week. She worked 40hours at her regular rate and 9 hours at a time and a half rate. Find her regular hourly rate.
Let the regular hourly rate be h. We're given:
40h + 40(1.5)(h - 40) = 642
Multiply through and simplify:
40h + 60h - 2400 = 642
100h - 2400 = 642
[URL='https://www.mathcelebrity.com/1unk.php?num=100h-2400%3D642&pl=Solve']To solve for h, we type this equation into our search engine[/URL] and we get:
h = [B]30.42[/B]

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add the

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add their ages is equal 100
Let the man's age be m. Let the wife's age be w. Let the daughter's age be d. We're given:
[LIST=1]
[*]m = w + 5
[*]d = 0.5m
[*]d + m + w = 100
[/LIST]
Rearrange equation 1 in terms of w my subtracting 5 from each side:
[LIST=1]
[*]w = m - 5
[*]d = 0.5m
[*]d + m + w = 100
[/LIST]
Substitute equation (1) and equation (2) into equation (3)
0.5m + m + m - 5 = 100
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.5m%2Bm%2Bm-5%3D100&pl=Solve']type this equation into our search engine[/URL] to solve for m and we get:
m = [B]42
[/B]
Now, substitute m = 42 into equation 2 to solve for d:
d = 0.5(42)
d = [B]21
[/B]
Now substitute m = 42 into equation 1 to solve for w:
w = 42 - 5
w = [B]37
[/B]
To summarize our ages:
[LIST]
[*]Man (m) = 42 years old
[*]Daughter (d) = 21 years old
[*]Wife (w) = 37 years old
[/LIST]

A man's age (a) 10 years ago is 43

A man's age (a) 10 years ago is 43
[U]10 years ago means we subtract 10 from a:[/U]
a - 10
[U]The word [I]is[/I] means an equation. So we set a - 10 equal to 43 to get our algebraic expression[/U]
[B]a - 10 = 43[/B]
If the problem asks you to solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=a-10%3D43&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = 53

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produced. The product sells for $22/unit.
The cost function for each unit u is:
C(u) = Variable Cost * Units + Fixed Cost
C(u) = 10u + 100000
The revenue function R(u) is:
R(u) = 22u
We want the break-even point, which is where:
C(u) = R(u)
10u + 100000 = 22u
[URL='https://www.mathcelebrity.com/1unk.php?num=10u%2B100000%3D22u&pl=Solve']Typing this equation into our search engine[/URL], we get:
u =[B]8333.33[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produced. The product sells for $20/unit
[U]Cost Function C(u) where u is the number of units:[/U]
C(u) = cost per unit * u + fixed cost
C(u) = 12u + 100000
[U]Revenue Function R(u) where u is the number of units:[/U]
R(u) = Sale price * u
R(u) = 20u
Break even point is where C(u) = R(u):
C(u) = R(u)
12u + 100000 = 20u
To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=12u%2B100000%3D20u&pl=Solve']type this equation into our search engine[/URL] and we get:
u = [B]12,500[/B]

A math teacher bought 40 calculators at $8.20 each and a number of other calculators costing$2.95 ea

A math teacher bought 40 calculators at $8.20 each and a number of other calculators costing$2.95 each. In all she spent $387. How many of the cheaper calculators did she buy
Let the number of cheaters calculators be c. Since amount equals price * quantity, we're given the following equation:
8.20 * 40 + 2.95c = 387
To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=8.20%2A40%2B2.95c%3D387&pl=Solve']type it in our search engine [/URL]and we get:
c = [B]20[/B]

A mechanic charges $50 to inspect your heater, plus $80 per hour to work on it. You owe the mechani

A mechanic charges $50 to inspect your heater, plus $80 per hour to work on it. You owe the mechanic a total of $310. Write and solve an equation to find the amount of time h (in hours) the mechanic works on your heater.
We calculate the cost function C(h) as:
C(h) = Hourly Rate * hours + Flat Fee Inspection
C(h) = 80h + 50 <-- this is our cost equation
Now, we want to solve for h when C(h) = 310
80h + 50 = 310
[URL='https://www.mathcelebrity.com/1unk.php?num=80h%2B50%3D310&pl=Solve']We type this equation into our search engine[/URL] and we get:
h = [B]3.25[/B]

A mechanic will charge a new customer $45.00 for an initial diagnosis plus $20 an hour of labor. How

A mechanic will charge a new customer $45.00 for an initial diagnosis plus $20 an hour of labor. How long did the mechanic work on a car if he charged the customer $165?
We set up a cost function C(h) where h is the number of hours of labor:
C(h) = Hourly Labor Rate * h + Initial Diagnosis
C(h) = 20h + 45
The problem asks for the number of hours if C(h) = 165. So we set our cost function C(h) above equal to 165:
20h + 45 = 165
To solve for h, [URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B45%3D165&pl=Solve']we plug this equation into our search engine[/URL] and we get:
h = [B]6[/B]

A mother duck lines her 13 ducklings up behind her. In how many ways can the ducklings line up

A mother duck lines her 13 ducklings up behind her. In how many ways can the ducklings line up?
In position one, we can have any of the 13 ducks.
In position two, we can have 12 ducks, since one has to occupy position one.
We subtract 1 each time until we fill up all 13 positions.
We have:
13 * 12 * 11 * ... * 2 * 1
Or, 13!. [URL='https://www.mathcelebrity.com/factorial.php?num=13!&pl=Calculate+factorial']Typing 13! into our search engine[/URL], we get [B]6,227,020,800[/B] ways the ducklings can line up behind the mother duck.

A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going dow

A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
[U]Assumptions:[/U]
[LIST]
[*]B = the speed of the boat in still water.
[*]S = the speed of the stream
[/LIST]
Relative to the bank, the speeds are:
[LIST]
[*]Upstream is B - S.
[*]Downstream is B + S.
[/LIST]
[U]Use the Distance equation: Rate * Time = Distance[/U]
[LIST]
[*]Upstream: (B-S)6 = 258
[*]Downstream: (B+S)6 = 330
[/LIST]
Simplify first by dividing each equation by 6:
[LIST]
[*]B - S = 43
[*]B + S = 55
[/LIST]
Solve this system of equations by elimination. Add the two equations together:
(B + B) + (S - S) = 43 + 55
Cancelling the S's, we get:
2B = 98
Divide each side by 2:
[B]B = 49 mi/hr[/B]
Substitute this into either equation and solve for S.
B + S = 55
49 + S = 55
To solve this, we [URL='https://www.mathcelebrity.com/1unk.php?num=49%2Bs%3D55&pl=Solve']type it in our search engine[/URL] and we get:
S = [B]6 mi/hr[/B]

A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pa

A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pass for $80. How many days must he work (i.e. pass through the toll) in order to break even?
Let the number of days be d. Break even means both costs are equal. We want to find when:
4.75d = 80
To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=4.75d%3D80&pl=Solve']type this equation into our search engine[/URL] and we get:
d = 16.84 days
We round up to an even [B]17 days[/B].

A new car worth $24,000 is depreciating in value by $3,000 per year , how many years till the cars v

A new car worth $24,000 is depreciating in value by $3,000 per year , how many years till the cars value will be $9,000
We have a flat rate depreciation each year. Set up the function D(t) where t is the number of years of depreciation:
D(t) = 24000 - 3000t
The problem asks for the time (t) when D(t) = 9000. So we set D(t) = 9000
24000 - 3000 t = 9000
To solve for t, [URL='https://www.mathcelebrity.com/1unk.php?num=24000-3000t%3D9000&pl=Solve']we plug this function into our search engine[/URL] and we get:
t = [B]5[/B]

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the pro

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 3 and the coin toss is heads? Write your answer as a fraction in simplest form
Let's review the vitals of this question:
[LIST]
[*]The probability of heads on a fair coin is 1/2.
[*]On a fair die, greater than 3 means either 4, 5, or 6. Any die roll face is a 1/6 probability.
[*]So we have a combination of outcomes below:
[/LIST]
Outcomes
[LIST=1]
[*]Heads and 4
[*]Heads and 5
[*]Heads and 6
[/LIST]
For each of the outcomes, we assign a probability. Since the coin flip and die roll are independent, we multiply the probabilities:
[LIST=1]
[*]P(Heads and 4) = 1/2 * 1/6 = 1/12
[*]P(Heads and 5) = 1/2 * 1/6 = 1/12
[*]P(Heads and 6) = 1/2 * 1/6 = 1/12
[/LIST]
Since we want any of those events, we add all three probabilities
1/12 + 1/12 + 1/12 = 3/12
This fraction is not simplified. S[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F12&frac2=3%2F8&pl=Simplify']o we type this fraction into our search engine, and choose Simplify[/URL].
We get a probability of [B]1/4[/B].
By the way, if you need a decimal answer or percentage answer instead of a fraction, we type in the following phrase into our search engine:
[URL='https://www.mathcelebrity.com/perc.php?num=1&den=4&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']1/4 to decimal[/URL]
Alternative Answers:
[LIST]
[*]For a decimal, we get [B]0.25[/B]
[*]For a percentage, we get [B]25%[/B]
[/LIST]

A park bench is 6 feet long. Convert the length to inches

A park bench is 6 feet long. Convert the length to inches
We [URL='https://www.mathcelebrity.com/linearcon.php?quant=6&pl=Calculate&type=foot']type in 6 feet into our search engine[/URL]. We get:
6 feet = [B]72 inches[/B]

A person that runs for 15 minutes burns 180 calories. If someone burns 300 calories, how long did tg

A person that runs for 15 minutes burns 180 calories. If someone burns 300 calories, how long did tgey run for
Set up a proportion of minutes to calories where m is the number of minutes per 300 calories:
15/180 = m/300
To solve for m, [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=m&den1=180&den2=300&propsign=%3D&pl=Calculate+missing+proportion+value']we type this proportion into our search engine[/URL] and we get:
m = [B]25[/B]

A person works 46 hours in one week and earns 440 dollars. They get time and a half for over 40 hour

A person works 46 hours in one week and earns 440 dollars. They get time and a half for over 40 hours. What is their hourly salary?
Let the hourly rate be r. Since time and a half is 1.5 the hourly rate, We're given:
40r + 6(1.5r) = 440
40r + 9r = 440
to solve this equation for r, we type it in our search engine and we get:
r = [B]$8.98[/B]

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the custome

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 8 cents per minute of use. In Plan B, the customer pays a monthly fee of $1.50 and then an additional 7 cents per minute of use.
For what amounts of monthly phone use will Plan A cost more than Plan B?
Set up the cost equations for each plan. The cost equation for the phone plans is as follows:
Cost = Cost Per Minute * Minutes + Monthly Fee
Calculate the cost of Plan A:
Cost for A = 0.08m + 0. <-- Since there's no monthly fee
Calculate the cost of Plan B:
Cost for B = 0.07m + 1.50
The problem asks for what amounts of monthly phone use will Plan A be more than Plan B. So we set up an inequality:
0.08m > 0.07m + 1.50
[URL='https://www.mathcelebrity.com/1unk.php?num=0.08m%3E0.07m%2B1.50&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]m > 150
This means Plan A costs more when you use more than 150 minutes per month.[/B]

A photographer snapped 224 photos over a period of 15 days. At this rate, how many would he take in

A photographer snapped 224 photos over a period of 15 days. At this rate, how many would he take in 45 days?
Set up a proportion of photos to days where p is the number of photos snapped in 45 days:
224/15 = p/45
To solve this proportion for p, we [URL='https://www.mathcelebrity.com/prop.php?num1=224&num2=p&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get;
p = [B]672[/B]

A plant is 15 cm high and grows 4.5 cm every month. How many months will it take until the plant is

A plant is 15 cm high and grows 4.5 cm every month. How many months will it take until the plant is 27.5 cm
We set up the height function H(m) where m is the number of months since now. We have:
H(m) = 4.5m + 15
We want to know when H(m) = 27.5, so we set our H(m) function equal to 27.5:
4.5m + 15 = 27.5
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=4.5m%2B15%3D27.5&pl=Solve']type this equation into our search engine[/URL] and we get:
m = 2.78
So we round up to [B]3 whole months[/B]

A police officer is trying to catch a fleeing criminal. The criminal is 20 feet away from the cop, r

A police officer is trying to catch a fleeing criminal. The criminal is 20 feet away from the cop, running at a rate of 5 feet per second. The cop is running at a rate of 6.5 feet per second. How many seconds will it take for the police officer to catch the criminal?
Distance = Rate * Time
[U]Criminal:[/U]
5t + 20
[U]Cop[/U]:
6.5t
We want to know when their distances are the same (cop catches criminal). So we set the equations equal to each other:
5t + 20 = 6.5t
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=5t%2B20%3D6.5t&pl=Solve']we type it in our search engine[/URL] and we get:
t = 13.333 seconds

A pollster selected 4 of 7 people. How many different groups of 4 are possible?

A pollster selected 4 of 7 people. How many different groups of 4 are possible?
We want to use the combinations formula. [URL='https://www.mathcelebrity.com/permutation.php?num=7&den=4&pl=Combinations']So we type 7C4 into our search engine[/URL]. This is also known as 7 choose 4.
We get [B]35[/B] different groups.

A population grows at 6% per year. How many years does it take to triple in size?

A population grows at 6% per year. How many years does it take to triple in size?
With a starting population of P, and triple in size means 3 times the original, we want to know t for:
P(1.06)^t = 3P
Divide each side by P, and we have:
1.06^t = 3
Typing this equation into our search engine to solve for t, we get:
t = [B]18.85 years[/B]
Note: if you need an integer answer, we round up to 19 years

A printer can print 25 pages per minute. At this rate, how long will it take to print 2000 pages?

A printer can print 25 pages per minute. At this rate, how long will it take to print 2000 pages?
Let m be the number of minutes it takes to print 2,000 pages. We have the equation:
25m = 2000
[URL='https://www.mathcelebrity.com/1unk.php?num=25m%3D2000&pl=Solve']Type this equation into our search engine[/URL], and we get:
m = 80

A problem states: "There are 9 more children than parents in a room. There are 25 people in the room

A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?"
Let the number of children be c. Let the number of parents be p
We're given:
[LIST=1]
[*]c = p + 9 [I](9 more children than parents)[/I]
[*]c + p = 25
[/LIST]
to solve this system of equations, we plug equation (1) into equation (2) for c:
(p + 9) + p = 25
Group like terms:
2p + 9 = 25
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=2p%2B9%3D25&pl=Solve']type it in our search engine[/URL] and we get:
p = [B]8[/B]

A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for

A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for all calls. If Joe's phone bill was $60 under this promotional deal, how many minutes of phone calls did he make? Round to the nearest integer if necessary.
Let m be the number of minutes Joe used. We have a cost function of:
C(m) = 0.05m + 15
If C(m) = 60, then we have:
0.05m + 15 = 60
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05m%2B15%3D60&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = [B]900[/B]

A quarter of a number is greater than or equal to 38

A quarter of a number is greater than or equal to 38.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
A quarter of a number means 1/4, so we have:
x/4
The phrase [I]is greater than or equal to[/I] means an inequality, so we use the >= sign in relation to 38:
[B]x/4 >= 38 <-- This is our algebraic expression
[/B]
If you want to solve this inequality, [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=38&propsign=%3E%3D&den1=4&den2=1&pl=Calculate+missing+proportion+value']we type it in the search engine[/URL] to get:
x >= [B]152[/B]

A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you ge

A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you get 92. What is the number?
Let the rational number be x. We're given:
7x/3 - 3/2 = 92
Using a common denominator of 3*2 = 6, we rewrite this as:
14x/6 - 9/6 = 92
(14x - 9)/6 = 92
Cross multiply:
14x - 9 = 92 * 6
14x - 9 = 552
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=14x-9%3D552&pl=Solve']type this equation into our search engine [/URL]and we get:
x = [B]40.07[/B]

A real estate agent has $920 to spend on newspaper ads. Each ad costs $6. After buying as many ads a

A real estate agent has $920 to spend on newspaper ads. Each ad costs $6. After buying as many ads as she can afford, how much money will the real estate agent have left over?
We want to know the remainder of 920/6. We can type 920 mod 6 into our search engine and get:
[URL='https://www.mathcelebrity.com/modulus.php?num=920mod6&pl=Calculate+Modulus']920 mod 6[/URL] = [B]2[/B]

A recipie calls for 2 tablespoons of olive oil for every 3 servings. How much olive oil will be nee

A recipe calls for 2 tablespoons of olive oil for every 3 servings. How much olive oil will be needed for 6 servings?
Set up a proportion of tablespoons to servings:
2/3 = o/6 where o is the number of tablespoons per 6 servings.
[URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=o&den1=3&den2=6&propsign=%3D&pl=Calculate+missing+proportion+value']Type 2/3 = o/6 into our search engine[/URL], and we get [B]o = 4[/B].

A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSION

A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSIONS OF THE RECTANGLE?
Whoa... stop screaming with those capital letters! But I digress...
The perimeter of a rectangle is:
P = 2l + 2w
We're given two equations:
[LIST=1]
[*]P = 196
[*]l = 6w
[/LIST]
Plug these into the perimeter formula:
2(6w) + 2w = 196
12w + 2w = 196
[URL='https://www.mathcelebrity.com/1unk.php?num=12w%2B2w%3D196&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]w = 14[/B]
Now we put w = 14 into equation (2) above:
l = 6(14)
[B]l = 84
[/B]
So our length (l), width (w) of the rectangle is (l, w) = [B](84, 14)
[/B]
Let's check our work by plugging this into the perimeter formula:
2(84) + 2(14) ? 196
168 + 28 ? 196
196 = 196 <-- checks out

A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards b

A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards because of a building code, what will the length need to be?
Perimeter of a rectangle (P) with length (l) and width (w) is:
2l + 2w = P
We're given P = 506 and w = 100. We plug this in to the perimeter formula and get:
2l + 2(100) = 506
To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B2%28100%29%3D506&pl=Solve']type it in our search engine[/URL] and we get:
l = [B]153[/B]

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 fe

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 feet longer than the width, then how wide is the field?
We're given:
[LIST=1]
[*]l = w + 40
[/LIST]
And we know the perimeter of a rectangle is:
P = 2l + 2w
Substitute (1) into this formula as well as the given perimeter of 1120:
2(w + 40) + 2w = 1120
Multiply through and simplify:
2w + 80 + 2w = 1120
Group like terms:
4w + 80 = 1120
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B80%3D1120&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 260[/B]

A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find i

A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find its length and width.
The area of a rectangle (A) is:
A = lw --> where l is the length and w is the width
We're given l = 2w, so we substitute this into the Area equation:
A = (2w)w
A = 2w^2
We're given the area of the pitch is 360, so we set:
2w^2 = 360
We [URL='https://www.mathcelebrity.com/1unk.php?num=2w%5E2%3D360&pl=Solve']type this equation into our search engine[/URL], follow the links, and get:
w = [B]6*sqrt(5)
[/B]
Now we take this, and substitute it into this equation:
6*sqrt(5)l = 360
Dividing each side by 6*sqrt(5), we get:
l = [B]60/sqrt(5)[/B]

A rectangular parking lot has a perimeter of 152 yards. If the length of the parking lot is 12 yards

A rectangular parking lot has a perimeter of 152 yards. If the length of the parking lot is 12 yards greater than the width. What is the width of the parking lot?
The perimeter of a rectangle is: 2l + 2w = P.
We're given 2 equations:
[LIST=1]
[*]2l + 2w = 152
[*]l = w + 12
[/LIST]
Substitute equation (2) into equation (1) for l:
2(w + 12) + 2w = 152
2w + 24 + 2w = 152
Combine like terms:
4w + 24 = 152
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B24%3D152&pl=Solve']type this equation into our search engine[/URL] and we get:
w =[B] 32[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters.

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters.
We're given the following:
[LIST]
[*]l = 3w
[/LIST]
We know the Perimeter (P) of a rectangle is:
P = 2l + 2w
Substituting l = 3w and P = 56 into this equation, we get:
2(3w) + 2w = 56
Multiplying through, we get:
6w + 2w = 56
(6 +2)w = 56
8w = 56
[URL='https://www.mathcelebrity.com/1unk.php?num=8w%3D56&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 7[/B]
Substitute w = 7 into l = 3w, we get:
l = 3(7)
[B]l = 21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimens

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimensions of the room.
We're given two items:
[LIST]
[*]l = 3w
[*]P = 56
[/LIST]
We know the perimeter of a rectangle is:
2l + 2w = P
We plug in the given values l = 3w and P = 56 to get:
2(3w) + 2w = 56
6w + 2w = 56
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']plug this equation into our search engine[/URL] and we get:
w = [B]7
[/B]
To solve for l, we plug in w = 7 that we just found into the given equation l = 3w:
l = 3(7)
l = [B]21
[/B]
So our dimensions length (l) and width (w) are:
(l, w) = [B](21, 7)[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimens

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimension of the room.
We're given:
l = 3w
The Perimeter (P) of a rectangle is:
P = 2l + 2w
With P = 56, we have:
[LIST=1]
[*]l = 3w
[*]2l + 2w = 56
[/LIST]
Substitute equation (1) into equation (2) for l:
2(3w) + 2w = 56
6w + 2w = 56
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']type it in our search engine[/URL] and we get:
w = [B]7
[/B]
Now we plug w = 7 into equation (1) above to solve for l:
l = 3(7)
l = [B]21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 64 meters. Find the dimens

A rectangular room is 3 times as long as it is wide, and its perimeter is 64 meters. Find the dimension of the room.
We're given:
[LIST]
[*]l = 3w
[*]P = 64
[/LIST]
We also know the perimeter of a rectangle is:
2l + 2w = P
We plugin l = 3w and P = 64 into the perimeter equation:
2(3w) + 2w = 64
Multiply through to remove the parentheses:
6w + 2w = 64
To solve this equation for w, we type it in our search engine and we get:
[B]w = 8[/B]
To solve for l, we plug w = 8 into the l = 3w equation above:
l = 3(8)
[B]l = 24[/B]

A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimens

A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimension of the room
The perimeter of a rectangle is P = 2l + 2w. We're given two equations:
[LIST=1]
[*]l = 4w
[*]2l + 2w = 80. <-- Since perimeter is 80
[/LIST]
Plug equation (1) into equation (2) for l:
2(4w) + 2w = 80
8w + 2w = 80
[URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B2w%3D80&pl=Solve']Plugging this equation into our search engine[/URL], we get:
w = [B]10[/B]
To get l, we plug w = 10 into equation (1):
l = 4(10)
l = [B]40[/B]

A rental truck costs $49.95+$0.59 per mile and another costs $39.95 plus $0.99, set up an equation t

A rental truck costs $49.95+$0.59 per mile and another costs $39.95 plus $0.99, set up an equation to determine the break even point?
Set up the cost functions for Rental Truck 1 (R1) and Rental Truck 2 (R2) where m is the number of miles
R1(m) = 0.59m + 49.95
R2(m) = 0.99m + 39.95
Break even is when we set the cost functions equal to one another:
0.59m + 49.95 = 0.99m + 39.95
[URL='https://www.mathcelebrity.com/1unk.php?num=0.59m%2B49.95%3D0.99m%2B39.95&pl=Solve']Typing this equation into the search engine[/URL], we get [B]m = 25[/B].

A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour. Write an

A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour. Write and solve an equation to find the number of hours spent repairing the car.
Let h be the number of hours spent repairing the car. We set up the cost function C(h):
C(h) = Labor Cost per hour * h + Parts Cost
We're given C(h) = 648.85, parts cost = 265.95, and labor cost per hour of 85, so we have:
85h + 265.95 = 648.85
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=85h%2B265.95%3D648.85&pl=Solve']type this into our search engine[/URL] and we get:
h = [B]4.5[/B]

A researcher believed that there was a difference in the amount of time boys and girls at 7th grade

A researcher believed that there was a difference in the amount of time boys and girls at 7th grade studied by using a two-tailed t test. Which of the following is the null hypothesis?
a. Mean of hours that boys studied per day was equal to mean of hours that girls studied per day
b. Mean of hours that boys studied per day was greater than mean of hours that girls studied per day
c. Mean of hours that boys studied per day was smaller than mean of hours that girls studied per day
d. Mean of hours that boys studied per day was smaller than or equal to mean of hours that girls studied per day
[B]a. Mean of hours that boys studied per day was equal to mean of hours that girls studied per day[/B]
Reason is that in hypothesis testing, you take a position other than what is assumed or what is being tested as the null hypothesis

A researcher posed a null hypothesis that there was no significant difference between boys and girls

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 120 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 6.0. What's the absolute value of the difference between means?
|70 -65| = |5| = 5

A researcher posed a null hypothesis that there was no significant difference between boys and girls

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What is the standard error of the difference in means?
[B]0.707106781187[/B] using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+100&xbar1=70&stdev1=5&n2=+100&xbar2=65&stdev2=5&conf=+99&pl=Hypothesis+Test']difference of means calculator[/URL]

A researcher posed a null hypothesis that there was no significant difference between boys and girls

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What's the t-value (two-tailed) for the null hypothesis that boys and girls have the same test scores?
t = 7.07106781187 using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+100&xbar1=70&stdev1=5&n2=+100&xbar2=65&stdev2=5&conf=+99&pl=Hypothesis+Test']difference of means calculator[/URL]

A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the am

A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount x (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period.
Let Sunday's earnings be s. With 3 days, we divide our sum of earnings for 3 days by 3 to get our 1,000 average, so we have:
(1073 + 1108 + s)/3 = 1000
Cross multiply:
1073 + 1108 + s = 1000 * 3
1073 + 1108 + s = 3000
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=1073%2B1108%2Bs%3D3000&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]819[/B]

A restaurant has 8 pizza toppings to choose from. How many different 2 topping pizzas are possible?

A restaurant has 8 pizza toppings to choose from. How many different 2 topping pizzas are possible?
We want 8 combinations of 2, denoted as 8 C 2, or 8 choose 2.
[URL='https://www.mathcelebrity.com/permutation.php?num=8&den=2&pl=Combinations']Typing 8 C 2 into the search engine[/URL], we get [B]28[/B] different 2 topping pizzas

A restaurant offers a special pizza with any 5 toppings. If the restaurant has 17 topping from which

A restaurant offers a special pizza with any 5 toppings. If the restaurant has 17 topping from which to choose, how many different special pizzas are possible?
We have 17 choose 5, or 17C5.
[URL='https://www.mathcelebrity.com/permutation.php?num=17&den=5&pl=Combinations']Type this into the search engine[/URL], and we get [B]6,188[/B] different special pizzas available.

A revenue function is R(x) = 22x and a cost function is C(x) = -9x + 341. The break-even point is

A revenue function is R(x) = 22x and a cost function is C(x) = -9x + 341. The break-even point is
Break even is when C(x) = R(x). So we set them equal and solve for x:
-9x + 341 = 22x
Typing[URL='https://www.mathcelebrity.com/1unk.php?num=-9x%2B341%3D22x&pl=Solve'] this equation into our search engine[/URL], we get:
x = [B]11[/B]

A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will excee

A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will exceed flood stage. How long can the river rise at this rate without exceeding flood stage?
Let the number of inches be i. Remember 12 inches to a foot, so we have 2 feet = 12*2 = 24 inches.
[LIST]
[*]Inequality: 3i <= 24. (since more than means the river can go [U]up to[/U] 2 feet or 24 inches
[/LIST]
To solve the inequality for I, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3i%3C%3D24&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]I <= 8
This means after 8 hours, the river will flood[/B]

a rocket is propelled into the air. its path can be modelled by the relation h = -5t^2 + 50t + 55, w

a rocket is propelled into the air. its path can be modeled by the relation h = -5t^2 + 50t + 55, where t is the time in seconds, and h is height in metres. when does the rocket hit the ground
We set h = 0:
-5t^2 + 50t + 55 = 0
Typing this quadratic equation into our search engine to solve for t, we get:
t = {-1, 11}
Time can't be negative, so we have:
t = [B]11[/B]

A roof drops 4 feet for every 12 feet forward. Determine the slope of the roof.

A roof drops 4 feet for every 12 feet forward. Determine the slope of the roof.
Slope = Rise or Drop / Run
Slope = 4/12
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F12&frac2=3%2F8&pl=Simplify']type 4/12 into our search engine[/URL] and get:
Slope. = [B]1/3[/B]

a sales rep can generate $1,900,000 in business annually. What rate of commission does he need to ea

a sales rep can generate $1,900,000 in business annually. What rate of commission does he need to earn $30,000?
We need a commission percent p where:
1900000 * p = 30000
To solve for p, we type this equation into our search engine and we get:
p = 0.0158 or [B]1.58%[/B]

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis?
Slope = Rise/Run or y/x
Since tests are on the y-axis and time is on the x-axis, we have:
Slope = 27/36
We can simplify this, so we [URL='https://www.mathcelebrity.com/fraction.php?frac1=27%2F36&frac2=3%2F8&pl=Simplify']type in 27/36 into our search engine[/URL], and get:
[B]Slope = 3/4[/B]

A school dance had 675 cookies each student took 3 cookies and there were 15 cookies leftover how ma

A school dance had 675 cookies each student took 3 cookies and there were 15 cookies leftover how many students attended the dance
Let each student be s. We have:
3s + 15 = 675
To solve this equation for s, [URL='https://www.mathcelebrity.com/1unk.php?num=3s%2B15%3D675&pl=Solve']we type it in our search engine[/URL] and we get:
s = [B]220[/B]

A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number?

A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number?
Take this algebraic expression in pieces:
[LIST]
[*]Let the secret number be n.
[*]Added to means we add 6 to n: n + 6
[*]The total is multiplied by 5: 5(n + 6)
[*]The phrase [I]to get[/I] means equal to, so we set 5(n + 6) equal to 50
[/LIST]
5(n + 6) = 50
To solve this equation for n, we type it in our search engine and we get:
n = [B]4[/B]

A service charges a $1.95 flat rate plus $0.05 per mile . Jason only has $12 to spend on a a ride

A service charges a $1.95 flat rate plus $0.05 per mile. Jason only has $12 to spend on a a ride.
Set up the cost equation C(m) where m is the number of miles:
C(m) = 0.05m + 1.95
The problems asks for the number of miles (m) when C(m) = 12:
0.05m + 1.95 = 12
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05m%2B1.95%3D12&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = [B]201[/B]

A set of data has a range of 30. The least value in the set of data is 22. What is the greatest valu

A set of data has a range of 30. The least value in the set of data is 22. What is the greatest value in the set of data?
High Value - Low Value = Range
Let the high value be h. We're given:
h - 22 = 30
We [URL='https://www.mathcelebrity.com/1unk.php?num=h-22%3D30&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]52[/B]

A single card is drawn from a standard 52 card deck. What is the possibility that the card drawn is

A single card is drawn from a standard 52 card deck. What is the possibility that the card drawn is either a 4 or a 6
There are 4 (4's) and 4 (6's) in a standard 52 card deck.
P(4 or 6) = P(4) + P(6)
P(4 or 6) = 4/52 + 4/52
P(4 or 6) = 8/52
We can simplify this fraction by [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F52&frac2=3%2F8&pl=Simplify']typing it in our search engine and choosing simplify[/URL]:
P(4 or 6) = [B]2/13[/B]

A soccer team lost 30% of their games and drew 15% and they played 67 games. How many games did they

A soccer team lost 30% of their games and drew 15% and they played 67 games. How many games did they win
If they lost 30% and they drew (tied) 15%, then they won the following:
Wins = 100% - Losses - Drew
Wins = 100% - 30% - 15%
Wins = 55%
So we want 55% of 67. We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=55&den1=67&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type this expression into our search engine[/URL] and we get:
[B]36.85 ~ 37 games[/B]

A spinner has 6 equal sections, of which 2 are green. If you spin the spinner once, what is the prob

A spinner has 6 equal sections, of which 2 are green. If you spin the spinner once, what is the probability that it will land on a green section? Write your answer as a fraction or whole number.
P(green) = Total Green / Total spaces
P(green) = 2/6
We can simplify this fraction. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F6&frac2=3%2F8&pl=Simplify']type 2/6 into our search engine[/URL], choose Simplify, and we get:
P(green) = [B]1/3[/B]

A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. What is

A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. What is the height of the box?
The volume of the box is l x w x h. We're given l and w = 4. So we want height:
56 = 4 x 4 x h
16h = 56
[URL='https://www.mathcelebrity.com/1unk.php?num=16h%3D56&pl=Solve']Type this equation into our search engine[/URL] and we get:
h = [B]3.5[/B]

A store sells small notebooks for $6 and large notebooks for $12. If a student buys 6 notebooks and

A store sells small notebooks for $6 and large notebooks for $12. If a student buys 6 notebooks and spends $60, how many of each did he buy?
Let the amount of small notebooks be s. Let the amount of large notebooks be l. We're given two equations:
[LIST=1]
[*]l + s = 6
[*]12l + 6s = 60
[/LIST]
Multiply equation (1) by -6
[LIST=1]
[*]-6l - 6s = -36
[*]12l + 6s = 60
[/LIST]
Now add equation 1 to equation 2:
12l - 6l + 6s - 6s = 60 - 36
Cancel the 6s terms, and we get:
6l = 24
To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=6l%3D24&pl=Solve']type this equation into our search engine[/URL] and we get:
l = [B]4
[/B]
Now substitute this into equation 1:
4 + s = 6
To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=4%2Bs%3D6&pl=Solve']we type this equation into our search engine[/URL] and we get:
s = [B]2[/B]

a student has $50 in saving and earns $40 per week. How long would it take them to save $450

a student has $50 in saving and earns $40 per week. How long would it take them to save $450
Set up the savings function S(w), where w is the number of weeks. The balance, S(w) is:
S(w) = Savings Per week * w + Initial Savings
S(w) = 40w + 50
The problems asks for how many weeks for S(w) = 450. So we have;
40w + 50 = 450
To solve for w, we[URL='https://www.mathcelebrity.com/1unk.php?num=40w%2B50%3D450&pl=Solve'] type this equation in our search engine[/URL] and we get:
w = [B]10[/B]

A super deadly strain of bacteria is causing the zombie population to double every day. Currently, t

A super deadly strain of bacteria is causing the zombie population to double every day. Currently, there are 25 zombies. After how many days will there be over 25,000 zombies?
We set up our exponential function where n is the number of days after today:
Z(n) = 25 * 2^n
We want to know n where Z(n) = 25,000.
25 * 2^n = 25,000
Divide each side of the equation by 25, to isolate 2^n:
25 * 2^n / 25 = 25,000 / 25
The 25's cancel on the left side, so we have:
2^n = 1,000
Take the natural log of each side to isolate n:
Ln(2^n) = Ln(1000)
There exists a logarithmic identity which states: Ln(a^n) = n * Ln(a). In this case, a = 2, so we have:
n * Ln(2) = Ln(1,000)
0.69315n = 6.9077
[URL='https://www.mathcelebrity.com/1unk.php?num=0.69315n%3D6.9077&pl=Solve']Type this equation into our search engine[/URL], we get:
[B]n = 9.9657 days ~ 10 days[/B]

A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand A aspirin. How many

A survey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand A aspirin. How many doctors use brand A aspirin?
We want 3/5 of 2000. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=2000&frac2=3/5&pl=Multiply']type this expression into our search engine[/URL] and we get:
[B]1,200[/B]

A sweater costs $40. That is 5 times as much as a shirt. What is the price of the shirt?

A sweater costs $40. That is 5 times as much as a shirt. What is the price of the shirt?
State this as an equation. Let the price of the shirt be s. 5 times as much means we multiply s by 5:
5s = 40
[URL='https://www.mathcelebrity.com/1unk.php?num=5s%3D40&pl=Solve']Type this equation into the search engine[/URL], we get:
s = [B]8[/B]

A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take

A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take for the tank to be empty
Assumptions and givens:
[LIST]
[*]Let the number of seconds be s.
[*]An empty tank means 0 liters of water.
[*]Leaks mean we subtract from the starting volume.
[/LIST]
We have the following relation:
800 - 12s = 0
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=800-12s%3D0&pl=Solve']type it in our search engine[/URL] and we get:
s = 66.67 seconds

A taxi cab in Chicago charges $3 per mile and $1 for every person. If the taxi cab ride for two peop

A taxi cab in Chicago charges $3 per mile and $1 for every person. If the taxi cab ride for two people costs $20. How far did the taxi cab travel.
Set up a cost function C(m) where m is the number of miles driven:
C(m) = cost per mile * m + per person fee
[U]Calculate per person fee:[/U]
per person fee = $1 per person * 2 people
per person fee = $2
[U]With a cost per mile of $3 and per person fee of $2, we have:[/U]
C(m) = cost per mile * m + per person fee
C(m) = 3m + 2
The problem asks for m when C(m) = 20, so we set 3m + 2 equal to 20:
3m + 2 = 20
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%2B2%3D20&pl=Solve']plug it in our search engine[/URL] and we get:
m = [B]6[/B]

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel?
Set up a cost function C(m), where m is the number of miles:
C(m) = Cost per mile * m + flat rate
C(m) = 0.65m + 1.75
The problem asks for m when C(m) = 10
0.65m + 1.75 = 10
[URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get:
m = [B]12.692 miles[/B]

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel
Set up a cost function C(m), where m is the number of miles Erica can travel. We have:
C(m) = 0.65m + 1.75
If C(m) = 10, we have:
0.65m + 1.75 = 10
[URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = 12.69 miles
If the problem asks for complete miles, we round down to 12 miles.

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel?
Set up the cost function C(m) where m is the number of miles:
C(m) = 0.65m + 1.75
If Erica has $10, then C(m) = 10, so we have:
0.65m + 1.75 = 10
[URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get
m = 12.69
if the answer asks for whole number, then we round down to m = 12

A taxi service charges an initial fee of $3 plus $1.80 per mile. How far can you travel for $12?

A taxi service charges an initial fee of $3 plus $1.80 per mile. How far can you travel for $12?
Given m for miles, we have the equation:
1.80m + 3 = 12
We [URL='https://www.mathcelebrity.com/1unk.php?num=1.80m%2B3%3D12&pl=Solve']type this equation into our search engine[/URL] to solve for m and we get:
m = [B]5[/B]

A teacher’s salary was $3300 after she had received an increase of 10%. Calculate the teacher’s sala

A teacher’s salary was $3300 after she had received an increase of 10%. Calculate the teacher’s salary if she has received an increase of 20% instead.
First, we need to find the starting salary. Let the starting salary be s. Since 10% as a decimal is 0.10, We're given:
s*(1.10) = 3300
1.10s = 3300
To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=1.10s%3D3300&pl=Solve']we type this equation into our search engine[/URL] and we get:
s = [B]3000[/B]
The problem asks for the new salary if the teacher's starting salary was increased by 20%. 20% as a decimal is 0.20, so we have:
3000(1.2) = $[B]3,600[/B]

A theater is 3/4 full. When 96 people leave, the theater is only 35% full. How many seat are there

A theater is 3/4 full. When 96 people leave, the theater is only 35% full. How many seats are there?
Let the full capacity of seats in the theater be s. We're given:
3/4s - 96 = 0.35s (Since 35% is 0.35)
We also know that 3/4 = 0.75, so let's use this to have decimals:
0.75s - 96 = 0.35s
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.75s-96%3D0.35s&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]240[/B]

A third of a pizza is 400 calories. How many calories in the whole pizza?

A third of a pizza is 400 calories. How many calories in the whole pizza?
Let c be the number of calories in the whole pizza. WE have:
c/3 = 400
To solve this proportion for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=c&num2=400&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and get:
c = [B]1,200[/B]

A toad croaks every 8seconds and a frog croaks every 6 seconds .They both croak at the same .After h

A toad croaks every 8seconds and a frog croaks every 6 seconds .They both croak at the same .After how many seconds will they next croak at the same time again.
We want the least common multiple of 8 and 6.
We type in [URL='https://www.mathcelebrity.com/gcflcm.php?num1=6&num2=8&num3=&pl=GCF+and+LCM']LCM(6, 8) into our search engine[/URL] and we get [B]24[/B]

A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was

A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was Marcos car towed if he received a bill for $71
Set up a cost equation C(m) where m is the number of miles:
C(m) = Cost per mile * m + Service Fee
Plugging in the service fee of 50 and cost per mile of 1.75, we get:
C(m) = 1.75m + 50
The question asks for what m is C(m) = 71. So we set C(m) = 71 and solve for m:
1.75m + 50 = 71
Solve for [I]m[/I] in the equation 1.75m + 50 = 71
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 50 and 71. To do that, we subtract 50 from both sides
1.75m + 50 - 50 = 71 - 50
[SIZE=5][B]Step 2: Cancel 50 on the left side:[/B][/SIZE]
1.75m = 21
[SIZE=5][B]Step 3: Divide each side of the equation by 1.75[/B][/SIZE]
1.75m/1.75 = 21/1.75
m = [B]12[/B]

A toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. T

A toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. The company sells each bear for $12.00 each. How many bears must this company sell in order to break even?
[U]Set up the cost function C(b) where b is the number of bears:[/U]
C(b) = Cost per bear * b + factory expenses
C(b) = 8b + 1500
[U]Set up the revenue function R(b) where b is the number of bears:[/U]
R(b) = Sale Price per bear * b
R(b) = 12b
[U]Break-even is where cost equals revenue, so we set C(b) equal to R(b) and solve for b:[/U]
C(b) = R(b)
8b + 1500 = 12b
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=8b%2B1500%3D12b&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]375[/B]

A train leaves San Diego at 1:00 PM. A second train leaves the same city in the same direction at 3

A train leaves San Diego at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 30mph faster than the first. If the second train overtakes the first at 6:00 PM, what is the speed of each of the two trains?
Distance = Rate x Time
Train 1:
d = rt
t = 1:oo PM to 6:00 PM = 5 hours
So we have d = 5r
Train 2:
d = (r + 30)t
t = 3:oo PM to 6:00 PM = 3 hours
So we have d = 3(r + 30)
Set both distances equal to each other since overtake means Train 2 caught up with Train 1, meaning they both traveled the same distance:
5r = 3(r + 30)
Multiply through:
3r + 90 = 5r
[URL='https://www.mathcelebrity.com/1unk.php?num=3r%2B90%3D5r&pl=Solve']Run this equation through our search engine[/URL], and we get [B]r = 45[/B]. This is Train 1's Speed.
Train 2's speed = 3(r + 30).
Plugging r = 45 into this, we get 3(45 + 30).
3(75)
[B]225[/B]

A tree grows 35 cm in 2 years. If it continues to grow at the same rate determine how long it would

A tree grows 35 cm in 2 years. If it continues to grow at the same rate determine how long it would take to grow 85 cm
We set up a proportion of cm to years where y is the number of years it takes to grow 85 cm:
35/2 = 85/y
To solve this proportion for y, [URL='https://www.mathcelebrity.com/prop.php?num1=35&num2=85&den1=2&den2=y&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
[B]y = 4.86[/B]

A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $

A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company?
Set up a cost function C(m) where m is the number of movies you rent:
C(m) = Rental cost per movie * m + Membership Fee
[U]Video Store 1 cost function[/U]
C(m) = 1m + 7.5
Video Store 2 cost function:
C(m) = 2.50m
We want to know when the costs are the same. So we set each C(m) equal to each other:
m + 7.5 = 2.50m
To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B7.5%3D2.50m&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]5[/B]

A water tank holds 236 gallons but is leaking at a rate of 3 gallons per week. A second water tank h

A water tank holds 236 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds 354 gallons but is leaking at a rate if 5 gallons per week. After how many weeks will the amount of water in the two tanks be the same
Let w be the number of weeks of leaking. We're given two Leak equations L(w):
[LIST=1]
[*]L(w) = 236 - 3w
[*]L(w) = 354 - 5w
[/LIST]
When the water in both tanks is the same, we can set both L(w) equations equal to each other:
236 - 3w = 354 - 5w
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=236-3w%3D354-5w&pl=Solve']type it in our search engine[/URL] and we get:
w = [B]59[/B]

A wildlife reserve has a population of 180 elephants. A group of researchers trapped 60 elephants an

A wildlife reserve has a population of 180 elephants. A group of researchers trapped 60 elephants and recorded their vital statistics. Of the trapped elephants, 12 were female. If that rate holds true for the entire population of 180 elephants, how many female elephants are on the wildlife reserve?
Set up a proportion of female to trapped elephants:
12/60 = f/180
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=12&num2=f&den1=60&den2=180&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we see that f = [B]36[/B]

A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages?

A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages?
Let the woman's age be w.
Let the mother's age be m.
We're given two equations:
[LIST=1]
[*]w = m/2
[*]m + w = 75
[/LIST]
Substitute equation (1) into equation (2) for w:
m + m/2 = 75
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%2F2%3D75&pl=Solve']type this equation into our search engine [/URL]and we get:
m = [B]50
[/B]
To solve for w, we plug m = 50 into equation (1):
w = 50/2
w = [B]25[/B]

A wood screw advances 1/16 inch for each complete turn. How far will the screw advance in 8 complete

A wood screw advances 1/16 inch for each complete turn. How far will the screw advance in 8 complete turns
1/6 inch per turn x 8 complete turns = 8/16.
Enter 8/16 into the search engine. Choose simplify. Using our [URL='http://www.mathcelebrity.com/fraction.php?frac1=8%2F16&frac2=3%2F8&pl=Simplify']simplify fraction calculator,[/URL] we get 8/16 simplified is [B]1/2[/B] of a turn.

Add 8 and 7, and then multiply by 2.

Add 8 and 7, and then multiply by 2.
Add 8 and 7:
8 + 7
Then multiply by 2:
2(8 + 7)
If you want to evaluate this order of operations, then [URL='https://www.mathcelebrity.com/distributive-property.php?a=2&b=8&c=7&pl=Distributive']type it in our search engine[/URL] to get:
[B]30[/B]

admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were col

admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were collected for a total of 10,078.75, how many students attended the fair
Let the number of students be s and the others be o. We're given two equations:
[LIST=1]
[*]o + s = 2848
[*]3.75o + 2.50s = 10078.75
[/LIST]
Since we have no coefficients for equation 1, let's solve this the fast way using substitution. Rearrange equation 1 by subtracting o from each side to isolate s
[LIST=1]
[*]o = 2848 - s
[*]3.75o + 2.50s = 10078.75
[/LIST]
Now substitute equation 1 into equation 2:
3.75(2848 - s) + 2.50s =10078.75
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3.75%282848-s%29%2B2.50s%3D10078.75&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]481[/B]

after buying some tickets for $19.00, Ann has $18.00 left. How much money did Ann have to beginwith

After buying some tickets for $19.00, Ann has $18.00 left. How much money did Ann have to begin with?
Let the beginning amount be b. We're given:
b - 19 = 18. <-- [I]We subtract 19 because a purchase is a spend reducing the original amount[/I]
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b-19%3D18&pl=Solve']type the equation b - 19 = 18 into our search engine [/URL]and we get:
b = [B]37[/B]

Age now and then

Yes, it was a bit odd. I'll do more research if she comes back on that one. I may have read it wrong. Let me know.

Ages are consecutive integers. The sum of ages are 111. What are the ages

Ages are consecutive integers. The sum of ages are 111. What are the ages
In the search engine, we type [I][URL='http://www.mathcelebrity.com/consecintwp.php?num=111&pl=Sum']sum of 2 consecutive integers is 111[/URL][/I].
We get [B]55 and 56[/B].

Al's Rentals charges $25 per hour to rent a sailboard and a wetsuit. Wendy's Rentals charges $20 per

Al's Rentals charges $25 per hour to rent a sailboard and a wetsuit. Wendy's Rentals charges $20 per hour plus $15 extra for a wetsuit. Find the number of hours for which the total charges for both companies would be the same.
Al's Rentals Cost Equation C(h) where h is the number of hours you rent a sailboard and wetsuit:
C(h) = 25h
Wendy's Rentals Cost Equation C(h) where h is the number of hours you rent a sailboard and wetsuit:
C(h) = 20h + 15
We want to set both cost equation equal to each other, and solve for h:
20h + 15 = 25h
[URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B15%3D25h&pl=Solve']Typing this equation into our search engine[/URL], we get:
h = [B]3[/B]

Alex says all factors of 16 are even why is she wrong

Alex says all factors of 16 are even why is she wrong.
[URL='https://www.mathcelebrity.com/factoriz.php?num=16&pl=Show+Factorization']Type in factor 16[/URL] into our search engine. We get the following factor of 16:
1, 2, 4, 8, 16
[B]All of these are even [I]except[/I] 1, which is odd. This is why Alex is wrong.[/B]

Ali needs to make a total of 90 deliveries this week. So far he has completed 72 of them. What perce

Ali needs to make a total of 90 deliveries this week. So far he has completed 72 of them. What percentage of his total deliveries has Ali completed
[URL='https://www.mathcelebrity.com/perc.php?num=72&den=90&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Enter 72/90 into our search engine and choose the percentage option[/URL] and we get [B]80%[/B].

Aliyah had $24 to spend on seven pencils. After buying them she had $1. How much did each pencil cos

Aliyah had $24 to spend on seven pencils. After buying them she had $1. How much did each pencil cost?
Let each pencil cost p. We're given the following equation:
7p + 1 = 24
[URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B1%3D24&pl=Solve']Type this equation into our search engine[/URL] and we get:
p = [B]$3.29[/B]

Aliyah has $24 to spend on 7 pencils. After buying them she had $10. How much did each pencil cost?

Aliyah has $24 to spend on 7 pencils. After buying them she had $10. How much did each pencil cost?
Let the cost of each pencil be p. The phrase [I]leftover[/I] means we add to the cost of the pencils after buying them. We're given the equation:
7p + 10 = 24
To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B10%3D24&pl=Solve']type this equation into our search engine[/URL] and we get:
p = [B]2[/B]

Allan built an additional room onto his house. The length of the room is 3 times the width. The peri

Allan built an additional room onto his house. The length of the room is 3 times the width. The perimeter of the room is 60 feet. What is the length of the room
A room is a rectangle. We know the perimeter of a rectangle is:
P = 2l + 2w
We're given two equations:
[LIST=1]
[*]l = 3w
[*]P = 60
[/LIST]
Plug (1) and (2) into our rectangle perimeter formula:
2(3w) + w = 60
6w + w = 60
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2Bw%3D60&pl=Solve']Type this equation into our search engine[/URL] to solve for w:
w = 8.5714
Now plug w = 8.5714 into equation 1 to solve for l:
l = 3(8.5714)
l = [B]25.7142[/B]

Alorah joins a fitness center. She pays for a year plus a joining fee of $35. If the cost for the en

Alorah joins a fitness center. She pays for a year plus a joining fee of $35. If the cost for the entire year is $299, how much will she pay each month?
We set up the cost function C(m) where m is the number of months of membership:
C(m) = cost per month * m + joining fee
Plugging in our numbers from the problem with 12 months in a year, we get:
12c + 35 = 299
To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=12c%2B35%3D299&pl=Solve']type it in our search engine [/URL]and we get:
c = [B]22[/B]

Alvin is 34 years younger than Elga. Elga is 3 times older than Alvin. What is Elgas age?

Alvin is 34 years younger than Elga. Elga is 3 times older than Alvin. What is Elgas age?
Let a be Alvin's age. Let e be Elga's age. We're given:
[LIST=1]
[*]a = e - 34
[*]e = 3a
[/LIST]
Substitute (2) into (1):
a = 3a - 34
[URL='https://www.mathcelebrity.com/1unk.php?num=a%3D3a-34&pl=Solve']Typing this equation into the search engine[/URL], we get
a = 17
Subtitute this into Equation (2):
e = 3(17)
e = [B]51[/B]

Alya loves to read. She reads 90 pages in half an hour. How many pages does she read per minute?

Alya loves to read. She reads 90 pages in half an hour. How many pages does she read per minute?
Set up a proportion of pages to minutes. Since 30 minutes is a half hour, we have the number of pages (p) for 1 minute as:
90/30 = p/1
To solve this proportion for p, [URL='https://www.mathcelebrity.com/prop.php?num1=90&num2=p&den1=30&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
p = [B]3[/B]

Alyssa had 87 dollars to spend on 6 books. After buying them she had 15 dollars . How much did each

Alyssa had 87 dollars to spend on 6 books. After buying them she had 15 dollars . How much did each book cost ?
Let b be the cost of each book. We're given:
87 - 6b = 15
[URL='https://www.mathcelebrity.com/1unk.php?num=87-6b%3D15&pl=Solve']Typing this equation into search engine[/URL], we get:
[B]b = 12[/B]

Amanda spent 2/5 of her time after school doing homework and ¼ of her remaining time riding her bike

Amanda spent 2/5 of her time after school doing homework and ¼ of her remaining time riding her bike. If she rode her bike for 45 minutes in a week, how much time did she devote to homework in the same week
If Amanda spent 2/5 of her time after school doing homework, she has 1 - 2/5 time left over.
We convert 1 to a fraction using a denominator of 5, we get:
5/5 - 2/5 = 3/5
And Amanda spent 1/4 of 3/5 of her time bike riding, which means she spent:
1(3)/4(5) = 3/20 of her time.
If the total time after school is t, we have:
3t/20 = 45
[URL='https://www.mathcelebrity.com/prop.php?num1=3t&num2=45&den1=20&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Typing in 3t/20 = 45 to our search engine[/URL], we get t = 300.
So Amanda has 300 total minutes after school, which means she spent 2/5(300) = [B]120 minutes (2 hours)[/B] doing homework.

Amar goes to the dance class every fourth day. Karan goes to the dance class every fifth day. Both m

Amar goes to the dance class every fourth day. Karan goes to the dance class every fifth day. Both met at the dance class today. After how many days will they meet at the dance class again?
We want the least common multiple of 4 and 5.
We type in [URL='https://www.mathcelebrity.com/gcflcm.php?num1=4&num2=5&num3=&pl=GCF+and+LCM']LCM(4,5)[/URL] into our search engine and we get [B]20.
So 20 days from now, Amar and Karen will meet again.[/B]

Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for ea

Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
Let the number of tv's be t. Set up the salary function S(t):
S(t) = Commision * tv's sold + Salary
Company A:
S(t) = 100t + 17,000
Company B:
S(t) = 20t + 29,000
The problem asks for how many tv's it takes to make both company salaries equal. So we set the S(t) functions equal to each other:
100t + 17000 = 20t + 29000
[URL='https://www.mathcelebrity.com/1unk.php?num=100t%2B17000%3D20t%2B29000&pl=Solve']Type this equation into our search engine[/URL] and we get:
t = [B]150[/B]

Amy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and in

Amy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and inside. Amy charges 40$ and Ryan charges 50$ . In addition they charge a hourly rate. Amy charges $35/h and ryan charges $30/h. How many hours does amy and ryan have to work to make the same amount of money?
Set up the cost functions C(h) where h is the number of hours.
[U]Amy:[/U]
C(h) = 35h + 40
[U]Ryan:[/U]
C(h) = 30h + 50
To make the same amount of money, we set both C(h) functions equal to each other:
35h + 40 = 30h + 50
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=35h%2B40%3D30h%2B50&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]2[/B]

An air horn goes off every 48 seconds,another every 80 seconds. At 5:00 pm the two go off simultaneo

An air horn goes off every 48 seconds,another every 80 seconds. At 5:00 pm the two go off simultaneously. At what time will the air horns blow again at the same time?
We want to find the least common multiple of (48, 80). So we [URL='https://www.mathcelebrity.com/gcflcm.php?num1=48&num2=80&num3=&pl=GCF+and+LCM']type this in our search engine[/URL], and we get:
240.
So 240 seconds is our next common meeting point for each air horn.
When we [URL='https://www.mathcelebrity.com/timecon.php?quant=240&pl=Calculate&type=second']type 240 seconds into our search engine[/URL], we get 4 minutes.
We add the 4 minutes to the 5:00 pm time to get [B]5:04 pm[/B].

An angle is 30 degrees less than 5 times it's complement. Find the angle.

An angle is 30 degrees less than 5 times it's complement. Find the angle.
Let the angle be a. The complement of a is 90 - a. We're given the following equation:
a = 5(90 - a) - 30 <-- Less means we subtract
Multiplying though, we get:
a = 450 - 5a - 30
a = 420 - 5a
[URL='https://www.mathcelebrity.com/1unk.php?num=a%3D420-5a&pl=Solve']Typing this equation into our search engine[/URL], we get:
a =[B] 70[/B]

An auto repair bill was $563. This includes $188 for parts and $75 for each hour of labor. Find the

An auto repair bill was $563. This includes $188 for parts and $75 for each hour of labor. Find the number of hours of labor
Let the number of hours of labor be h. We have the cost function C(h):
C(h) = Hourly Labor Rate * h + parts
Given 188 for parts, 75 for hourly labor rate, and 563 for C(h), we have:
75h + 188 = 563
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=75h%2B188%3D563&pl=Solve']type it in our search engine[/URL] and we get:
h = [B]5[/B]

An elevator has a maximum weight of 3000 pounds. How many 150-pound people can safely ride the eleva

An elevator has a maximum weight of 3000 pounds. How many 150-pound people can safely ride the elevator? (Use "p" to represent the number of people)
Maximum means less than or equal to. We have the inequality:
150p <= 3000
To solve this inequality for p, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=150p%3C%3D3000&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]p <= 20[/B]

An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumpin

An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumping it on the people below. One bucket dumps water every 18 minutes. The other bucket dumps water every 21 minutes. It is currently 1:15 P.M. and both buckets dumped water 5 minutes ago. Find the next two times that both buckets dump water at the same time.
We want to find the Least Common Multiple between 18 minutes and 21 minutes. This shows us when both bucket dumping cycles happen simultaneously. So we[URL='https://www.mathcelebrity.com/gcflcm.php?num1=18&num2=21&num3=&pl=GCF+and+LCM'] type in LCM(18,21) into our search engine and we get[/URL]:
LCM(18, 21) = 126
This means, in 126 minutes, both buckets will dump water. Since 60 minutes is in an hour, we find out how many full hours we have. To find the full hours and remainder, we [URL='https://www.mathcelebrity.com/modulus.php?num=126mod60&pl=Calculate+Modulus']type in 126 mod 60[/URL] into our search engine and we get:
6. This means 126 minutes is 2 hours and 6 minutes.
Find the next bucket dumping time:
[LIST=1]
[*]We start at 1:15 PM
[*]Add 2 hours and we get 3:15 PM
[*]Add 6 minutes and we get [B]3:21 PM[/B]
[/LIST]

An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the mea

An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the measure of all 3 angles?
Let the congruent angles measurement be c. And the non-congruent angle measurement be n. We're given:
[LIST=1]
[*]n = 2c + 16 <-- Twice means we multiply by 2, and more than means we add 16
[*]2c + n = 180 <-- Since the sum of angles in an isosceles triangle is 180
[/LIST]
Substitute (1) into (2):
2c + (2c + 16) = 180
Group like terms:
4c + 16 = 180
[URL='https://www.mathcelebrity.com/1unk.php?num=4c%2B16%3D180&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]c = 41[/B]
Substituting this value into Equation 1, we get
n = 2(41) + 16
n = 82 + 16
[B]n = 98[/B]

An orchard has 378 orange trees. The number of rows exceeds the number of trees per row by 3. How ma

An orchard has 378 orange trees. The number of rows exceeds the number of trees per row by 3. How many trees are there in each row?
We have r rows and t trees per row. We're give two equations:
[LIST=1]
[*]rt = 378
[*]r = t + 3
[/LIST]
Substitute equation (2) into equation (1) for r:
(t + 3)t = 378
Multiply through:
t^2 + 3t = 378
We have a quadratic equation. To solve this equation, we [URL='https://www.mathcelebrity.com/quadratic.php?num=t%5E2%2B3t%3D378&pl=Solve+Quadratic+Equation&hintnum=+0']type it in our search engine [/URL]and we get:
t = 18 and t = -21
Since t cannot be negative, we get trees per row (t):
[B]t = 18[/B]

An orchard has 816 apple trees. The number of rows exceeds the number of trees per row by 10. How ma

An orchard has 816 apple trees. The number of rows exceeds the number of trees per row by 10. How many trees are there in each row?
Let the rows be r and the trees per row be t. We're given two equations:
[LIST=1]
[*]rt = 816
[*]r = t + 10
[/LIST]
Substitute equation (2) into equation (1) for r:
(t + 10)t = 816
t^2 + 10t = 816
Subtract 816 from each side of the equation:
t^2 + 10t - 816 = 816 - 816
t^2 + 10t - 816 = 0
We have a quadratic equation. To solve this, we [URL='https://www.mathcelebrity.com/quadratic.php?num=t%5E2%2B10t-816%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type it in our search engine [/URL]and we get:
t = (24, -34)
Since the number of trees per row can't be negative, we choose [B]24[/B] as our answer

Ana's height is strictly between 63 and 66 inches. Write a symbolic inequality to represent this sce

Ana's height is strictly between 63 and 66 inches. Write a symbolic inequality to represent this scenario. let h be height
[B]63 < h < 66
[/B]
You can also type [I][URL='https://www.mathcelebrity.com/algexpress.php?num=between63and66&pl=Write+Expression']between 63 and 66[/URL][/I] in our search engine.

Andrea has one hour to spend training for an upcoming race she completes her training by running ful

Andrea has one hour to spend training for an upcoming race she completes her training by running full speed in the distance of the race and walking back the same distance to cool down if she runs at a speed of 9 mph and walks back at a speed of 3 mph how long should she plan on spending to walk back
Let r = running time. Let w = walking time
We're given two equations
[LIST=1]
[*]r + w = 1
[*]9r = 3w
[/LIST]
Rearrange equation (1) by subtract r from each side:
[LIST=1]
[*]w = 1 - r
[*]9r = 3w
[/LIST]
Now substitute equation (1) into equation (2):
9r = 3(1 - r)
9r = 3 - 3r
To solve for r, [URL='https://www.mathcelebrity.com/1unk.php?num=9r%3D3-3r&pl=Solve']we type this equation into our search engine[/URL] and we get:
r = 0.25
Plug this into modified equation (1) to solve for w, and we get:
w = 1. 0.25
[B]w = 0.75[/B]

Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What

Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What was the original number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it n.
[LIST]
[*]Start with n
[*]Add 20 to it: n + 20
[*]Double it means we multiply the expression by 2: 2(n + 20)
[*]Get an answer of 53: means an equation, so we set 2(n + 20) equal to 53
[/LIST]
2(n + 20) = 53
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%28n%2B20%29%3D53&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]6.5[/B]

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community col

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community college charges a $35 registration fee plus $375 per course, what is the greatest number of courses for which Angelica can register?
We set up the Tuition function T(c), where c is the number of courses:
T(c) = Cost per course * c + Registration Fee
T(c) = 35c + 375
The problem asks for the number of courses (c) where her tuition [I]cannot exceed[/I] $1000. The phrase [I]cannot exceed[/I] means less than or equal to, or no more than. So we setup the inequality for T(c) <= 1000 below:
35c + 375 <= 1000
To solve this inequality for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=35c%2B375%3C%3D1000&pl=Solve']type it in our search engine and we get[/URL]:
c <= 17.85
Since we cannot have fractional courses, we round down and get:
c[B] <= 17[/B]

Angelo is paid double time for each hour he works over 40 hours in a week. Last week he worked 46 ho

Angelo is paid double time for each hour he works over 40 hours in a week. Last week he worked 46 hours and earned $624. What is his normal hourly rate?
Let h be Angelo's hourly rate. We have:
40h + (46 - 40) * 2 * h = 624
40h + 6 * 2 * h = 624
40h + 12h = 624
Combine like terms:
52h = 624
[URL='https://www.mathcelebrity.com/1unk.php?num=52h%3D624&pl=Solve']Typing this equation into our search engine[/URL], we get [B]h = 12[/B].

Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Ke

Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Kenny buys 1 software package and 1 month of game play. Each software package costs $25. If their total cost is $155, what is the cost of one month of game play.
Let s be the cost of software packages and m be the months of game play. We have:
[LIST]
[*]Angie: 2s + 4m
[*]Kenny: s + m
[/LIST]
We are given each software package costs $25. So the revised equations above become:
[LIST]
[*]Angie: 2(25) + 4m = 50 + 4m
[*]Kenny: 25 + m
[/LIST]
Finally, we are told their combined cost is 155. So we add Angie and Kenny's costs together:
4m + 50 + 25 + m = 155
Combine like terms:
5m + 75 = 155
[URL='http://www.mathcelebrity.com/1unk.php?num=5m%2B75%3D155&pl=Solve']Typing this into our search engine[/URL], we get [B]m = 16[/B]

Angie knew 90% of the answers on a worksheet. What fraction of the answers did she know?

Angie knew 90% of the answers on a worksheet. What fraction of the answers did she know?
We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=90&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type [I]90% as a fraction[/I] into our search engine[/URL] and we get:
[B]9/10[/B]

Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a t

Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of $5 Ann paid a total of $49.10.
Set up the cost function C(m) where m is the number of miles:
C(m) = Mileage Rate x m + Tip
2.10m + 5 = 49.10
[URL='https://www.mathcelebrity.com/1unk.php?num=2.10m%2B5%3D49.10&pl=Solve']Type 2.10m + 5 = 49.10 into the search engine[/URL], and we get [B]m = 21[/B].

Anna has 50 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exa

Anna has 50 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exactly four times as many pennies as dimes, how many pennies are in her piggy bank?
Let d be the number of dimes, and p be the number of pennies. We're given:
[LIST=1]
[*]d + p = 50
[*]p = 4d
[/LIST]
Substitute (2) into (1)
d + 4d = 50
[URL='https://www.mathcelebrity.com/1unk.php?num=d%2B4d%3D50&pl=Solve']Type that equation into our search engine[/URL]. We get:
d = 10
Now substitute this into Equation (2):
p = 4(10)
[B]p = 40[/B]

Antonio has a change jar that contains $3.65 in half dollars and nickels. He has 7 more nickels than

Antonio has a change jar that contains $3.65 in half dollars and nickels. He has 7 more nickels than half dollars. How many of each type of coin does he have?
Let h be half dollars
Let n be nickels
We're given two equations:
[LIST=1]
[*]n = h + 7
[*]0.5h + 0.05n = 3.65
[/LIST]
Substitute equation (1) into equation (2) for n:
0.5h + 0.05(h + 7) = 3.65
To solve this equation for h, we[URL='https://www.mathcelebrity.com/1unk.php?num=0.5h%2B0.05%28h%2B7%29%3D3.65&pl=Solve'] type it in our search engine[/URL] and we get:
h = [B]6
[/B]
To get n, we substitute h = 6 into equation (1) above:
n = 6 + 7
n = [B]13[/B]

April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that

April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that June has. April has two-thirds of the number of sweets that May has. How many sweets does June have?
Let the April sweets be a.
Let the May sweets be m.
Let the June sweets be j.
We're given the following equations:
[LIST=1]
[*]m = 3j/4
[*]a = 2m/3
[*]a + j + m = 90
[/LIST]
Cross multiply #2;
3a = 2m
Dividing each side by 2, we get;
m = 3a/2
Since m = 3j/4 from equation #1, we have:
3j/4 = 3a/2
Cross multiply:
6j = 12a
Divide each side by 12:
a = j/2
So we have:
[LIST=1]
[*]m = 3j/4
[*]a = j/2
[*]a + j + m = 90
[/LIST]
Now substitute equation 1 and 2 into equation 3:
j/2 + j + 3j/4 = 90
Multiply each side by 4 to eliminate fractions:
2j + 4j + 3j = 360
To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%2B4j%2B3j%3D360&pl=Solve']type it in our search engine[/URL] and we get:
j = [B]40[/B]

Arc Length and Area of a Sector of a Circle

Calculates the arc length of a circle and the area of the sector of a circle

Arthur had $90. He spent $40 and gave $20 to his brother. What fraction of Arthur's money is left

Arthur had $90. He spent $40 and gave $20 to his brother. What fraction of Arthur's money is left?
Arthur starts with $90.
He gives away $40, so now he has $90 - $40 = $50.
Next, he gives $20 to his brother, so now he has $50 - $20 = $30.
So Arthur has 30/90 left.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=30%2F90&frac2=3%2F8&pl=Simplify']We type 30/90 into our search engine[/URL] and simplify to get:
[B]1/3[/B]

Arvin is twice as old as Cory. The sum of their ages is 42. What are their ages?

Arvin is twice as old as Cory. The sum of their ages is 42. What are their ages?
Let Arvin's age be a. Let Cory's age be c. We're given two equations:
[LIST=1]
[*]a = 2c
[*]a + c = 42
[/LIST]
Plug equation (1) into equation (2):
2c + c = 42
[URL='https://www.mathcelebrity.com/1unk.php?num=2c%2Bc%3D42&pl=Solve']Plug this into our search engine[/URL] and we get:
[B]c = 14[/B]
Now, we plug c = 14 into equation 1 to solve for a:
a = 2(14)
[B]a = 28[/B]

As a salesperson you will earn $600 per month plus a commission of 20% of sales. Find the minimum am

As a salesperson you will earn $600 per month plus a commission of 20% of sales. Find the minimum amount of sales you need to make in order to receive a total income of at least $1500 per month.
Let the amount of sales be s. The phrase [I]at least[/I] means greater than or equal to. Since 20% is 0.2, We want to know when:
0.20s + 600 >= 1500
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.20s%2B600%3E%3D1500&pl=Solve']type this inequality into our search engine to solve for s[/URL] and we get:
s >= [B]4500[/B]

Ashley age is 2 times Johns age. The sum of their ages is 63. What is Johns age?

Ashley age is 2 times Johns age. The sum of their ages is 63. What is Johns age?
Let Ashley's age be a.
Let John's age be j.
We have two equations:
[LIST=1]
[*]a = 2j
[*]a + j = 63
[/LIST]
Now substitute (1) into (2)
(2j) + j = 63
Combine like terms:
3j = 63
[URL='http://www.mathcelebrity.com/1unk.php?num=3j%3D63&pl=Solve']Typing 3j = 63 into our search engine[/URL], we get
[B]j = 21[/B]

At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 m

At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 more child tickets than adult tickets were sold. If a total of $6360 was collected from the total ticket sale that day, how many child tickets were sold?
Let the number of adult tickets be a. Let the number of child tickets be c. We're given two equations:
[LIST=1]
[*]c = a + 30
[*]6a + 4c = 6360
[/LIST]
Substitute equation (1) into equation (2):
6a + 4(a + 30) = 6360
Multiply through to remove parentheses:
6a + 4a + 120 = 6360
T[URL='https://www.mathcelebrity.com/1unk.php?num=6a%2B4a%2B120%3D6360&pl=Solve']ype this equation into our search engine[/URL] to solve for a and we get:
a = 624
Now substitute a = 624 back into equation (1) to solve for c:
c = 124 + 30
c = [B]154[/B]

At a concert there were 25 more women than men. The total number of people at the concert was 139. F

At a concert there were 25 more women than men. The total number of people at the concert was 139. Find the number of women and the number of men at the concert.
Let men be m and women be w. We're given two equations.
[LIST=1]
[*]w = m + 25
[*]m + w = 139
[/LIST]
Substitute equation (1) into equation (2):
m + m + 25 = 139
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%2B25%3D139&pl=Solve']type this equation into our search engine[/URL] and we get:
m = [B]57
[/B]
To find w, we substitute m = 57 into equation (1):
w = 57 + 25
w = [B]82[/B]

At a concert, 20% of the audience members were teenagers. If the number of teenagers at the concert

At a concert, 20% of the audience members were teenagers. If the number of teenagers at the concert was 360, what was the total number of audience members?
We're looking for total audience members where [I]20% of what equals 360[/I]?
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=360&pct1=20&pcheck=2&pct2=+70&den1=+80&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Type this expression into our search engine[/URL] and we get:
Audience = [B]1,800[/B]

At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers fo

At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers for $1.35 each. They sold 40 more slices of pizza than hamburgers, and sales totaled $292.5. How many slices of pizza did they sell
Let the number of pizza slices be p and the number of hamburgers be h. We're given two equations:
[LIST=1]
[*]p = h + 40
[*]1.35h + 0.75p = 292.50
[/LIST]
[I]Substitute[/I] equation (1) into equation (2) for p:
1.35h + 0.75(h + 40) = 292.50
1.35h + 0.75h + 30 = 292.50
2.10h + 30 = 292.50
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.10h%2B30%3D292.50&pl=Solve']plug this equation into our search engine[/URL] and we get:
h = 125
The problem asks for number of pizza slices sold (p). So we substitute our value above of h = 125 into equation (1):
p = 125 + 40
p = [B]165[/B]

At a light bulb factory 4 out of every 25 light bulbs are defective. How many light bulbs would you

At a light bulb factory 4 out of every 25 light bulbs are defective. How many light bulbs would you excpect to be defective out of 350 light bulbs
Set up a proportion of light bulbs to defects where d is the number of defects per 350 light bulbs:
4/25 = b/350
[URL='https://www.mathcelebrity.com/prop.php?num1=4&num2=b&den1=25&den2=350&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
b = [B]56[/B]

At Smith's Bike Rentals, it costs $40 to rent a bike for 9 hours. How many hours of bike use does a

At Smith's Bike Rentals, it costs $40 to rent a bike for 9 hours. How many hours of bike use does a customer get per dollar?
Hours / Dollar = 9/40
[URL='https://www.mathcelebrity.com/search.php?q=9%2F40&x=0&y=0']Hours/Dollar[/URL] = [B]22.5 cents or 23 cents[/B]

At the end of the day, the temperature is -16°C. During the day it dropped 12°C. What was the temper

At the end of the day, the temperature is -16°C. During the day it dropped 12°C. What was the temperature in the morning? Write an equation to represent, then solve and verify your answer
let the starting temperature be s. If the temperature dropped, that means we subtract, so we have the following equation:
s - 12 = -16
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=s-12%3D-16&pl=Solve']type it in our search engine[/URL] and we get:
s = [B]-4[/B]

At the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on

At the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on a movie and popcorn and another $1.35 on a pen. How much did she earn babysitting?
Let the original amount of money earned for babysitting be b. We're given:
[LIST=1]
[*]Start with b
[*]Spending 14.65 for a movie means we subtract 14.65 from b: b - 14.65
[*]Spending 1.35 on a pen means we subtract another 1.35 from step 2: b - 14.65 - 1.35
[*]Francesca has a third of her money left. So we set step 3 equal to 1/3 of b
[/LIST]
b - 14.65 - 1.35 = b/3
Multiply each side of the equation by 3 to remove the fraction
3(b - 14.65 - 1.35) = 3b/3
3b - 43.95 - 4.05 = b
To solve this equation for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b-43.95-4.05%3Db&pl=Solve']we type it in our search engine[/URL] and we get:
b =[B] 24[/B]

Austin needs $240 to buy a new bike if he can save $16 per week and how many weeks can you purchase

Austin needs $240 to buy a new bike if he can save $16 per week and how many weeks can you purchase the bike?
Set up the equation, where w equals the number of weeks needed. We have:
16w = 240
[URL='https://www.mathcelebrity.com/1unk.php?num=16w%3D240&pl=Solve']Typing this into our search engine[/URL], we get [B]w = 15[/B].

average of 16 and x is three. find x

average of 16 and x is three. find x
Average of 16 and x is written as:
(16 + x)/2
We set this equal to 3:
(16 + x)/2 = 3
Cross multiply;
x + 16 = 6
[URL='https://www.mathcelebrity.com/1unk.php?num=x%2B16%3D6&pl=Solve']Type this equation into our search engine[/URL] and we get:
x = [B]-10[/B]

Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign

Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign, then divided by 3. What was the original equation
[LIST=1]
[*]If we added 7 to both sides, that means we had a minus 7 (-7) to start with as a constant. Since subtraction undoes addition.
[*]If we divided by 3, this means we multiplied x by 3 to begin with. Since division undoes multiplication
[/LIST]
So we have the start equation:
3x - 7
If the answer was x = -4, then we plug this in to get our number on the right side of the equation:
3(-4) - 7
-12 - 7
-19
This means our original equation was:
[B]3x - 7 = -19[/B]
And if we want to solve this to prove our answer, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D-19&pl=Solve']type the equation into our search engine [/URL]and we get:
x = -4

Belen can make 15 necklaces in 3 1/2 hours. How many can she make in one hour?

Belen can make 15 necklaces in 3 1/2 hours. How many can she make in one hour?
We set up a proportion of necklaces to time, where n is the number of necklaces Belen can make in 1 hour:
3 & 1/2 = 3.5, so we have:
15/3.5 = n/1
[SIZE=3][FONT=Helvetica][COLOR=rgb(34, 34, 34)]
To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=n&den1=3.5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine and we ge[/URL]t:
n = [B]4.29 hours[/B][/COLOR][/FONT][/SIZE]

Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each p

Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each pencil
The cost per pencil is:
1560/30 = 52
Build revenue function:
Revenue = Number of Pencils * Sales Price (s)
Revenue = 30s
The profit equation is:
Profit = Revenue - Cost
Given profit is 180 and cost is 1560, we have:
30s - 1560 = 180
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=30s-1560%3D180&pl=Solve']type this equation into our search engine[/URL] and we get:
s = 58
This is sales for total profit. The question asks profit per pencil.
Profit per pencil = Revenue per pencil - Cost per pencil
Profit per pencil = 58 - 52
Profit per pencil = [B]6[/B]

Ben can write 153 letters in 3 minutes. At this rate, how many letters can he write in 10 minutes?

Ben can write 153 letters in 3 minutes. At this rate, how many letters can he write in 10 minutes?
We set up a proportion of letters to minutes where the number of letters in 10 minutes is l:
153/3 = l/10
We [URL='https://www.mathcelebrity.com/prop.php?num1=153&num2=l&den1=3&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into a search engine[/URL] and we get:
l =[B] 510[/B]

Ben is 3 times as old as Daniel and is also 4 years older than Daniel.

Ben is 3 times as old as Daniel and is also 4 years older than Daniel.
Let Ben's age be b, let Daniel's age by d. We're given:
[LIST=1]
[*]b = 3d
[*]b = d + 4
[/LIST]
Substitute (1) into (2)
3d = d + 4
[URL='https://www.mathcelebrity.com/1unk.php?num=3d%3Dd%2B4&pl=Solve']Type this equation into our search engine[/URL], and we get [B]d = 2[/B].
Substitute this into equation (1), and we get:
b = 3(2)
[B]b = 6
[/B]
So Daniel is 2 years old and Ben is 6 years old.

Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan.

Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan.
Let b be Ben's age and i be Ishaan's age. We're given:
[LIST=1]
[*]b = 4i
[*]b = i + 6
[/LIST]
Set (1) and (2) equal to each other:
4i = i + 6
[URL='https://www.mathcelebrity.com/1unk.php?num=4i%3Di%2B6&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]i = 2[/B]
Substitute this into equation (1):
b = 4(2)
[B]b = 8
[/B]
[I]Therefore, Ishaan is 2 years old and Ben is 8 years old.[/I]

Ben visits the park every 2 days and goes to the library every 5 days. If Ben gets to do both of the

Ben visits the park every 2 days and goes to the library every 5 days. If Ben gets to do both of these today, how many days will pass before Ben gets to do them both on the same day again?
To find this, we want the least common multiple (LCM) of 2 and 5. We [URL='https://www.mathcelebrity.com/gcflcm.php?num1=2&num2=5&num3=&pl=GCF+and+LCM']type LCM(2,5) into our search engine[/URL] and we get:
[B]10 days
[/B]
We check our work:
2 days * 5 visits = 10 days
5 days * 2 visits = 10 days

Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of

Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 47 cards left. How many cards did Benny start with?
Let b be the number of baseball trading cards Benny started with. We have the following events:
[LIST=1]
[*]Benny buys 8 new cards, so we add 8 to get b + 8
[*]The dog ate half of his cards the next day, so Benny has (b + 8)/2
[*]We're told he has 47 cards left, so we set (b + 8)/2 equal to 47
[/LIST]
(b + 8)/2 = 47
[B][U]Cross multiply:[/U][/B]
b + 8 = 47 * 2
b + 8 = 94
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B8%3D94&pl=Solve']Type this equation into the search engine[/URL], we get [B]b = 86[/B].

Benny had 90 dollars to spend on 7 books. After buying them he had 13 dollars. How much did each boo

Benny had 90 dollars to spend on 7 books. After buying them he had 13 dollars. How much did each book cost?
Let each book cost be b. We have:
7b + 13 = 90
[URL='https://www.mathcelebrity.com/1unk.php?num=7b%2B13%3D90&pl=Solve']Typing this equation into the search engine[/URL], and you get:
[B]b = 11[/B]

Beth is 5 years younger than celeste. Next year, their ages will have a sum equal to 57. How old is

Beth is 5 years younger than celeste. Next year, their ages will have a sum equal to 57. How old is each now?
Let b = Beth's age
Let c = Celeste's age
We are given:
[LIST=1]
[*]b = c - 5
[*]b + 1 + c + 1 = 57
[/LIST]
Substitute (1) into (2)
(c - 5) + 1 + c + 1 = 57
Group like terms:
2c - 3 = 57
[URL='https://www.mathcelebrity.com/1unk.php?num=2c-3%3D57&pl=Solve']Type 2c - 3 = 57 into our search engine[/URL], we get [B]c = 30[/B]
Substitute c = 30 into Equation (1), we get:
b = 30 - 5
[B]b = 25
[/B]
Therefore, Beth is 25 and Celeste is 30.

Beverly has $50 to spend at an amusement park. She plans to spend $10 for food, and $15 for admissio

Beverly has $50 to spend at an amusement park. She plans to spend $10 for food, and $15 for admission to the park. Each ride costs $1.50 to ride. Write an inequality to represent the possible number of rides she can ride?
First, we subtract the food and admission cost from Beverly's starting balance of $50:
Cost available for rides = Starting Balance - Food - Admission
Cost available for rides = 50 - 10 - 15
Cost available for rides = 25
Now we set up an inequality for the number of rides (r) that Beverly can ride with the remaining balance:
1.50r <= 25
To solve for r, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.50r%3C%3D25&pl=Show+Interval+Notation']type this inequality into our search engine[/URL] and we get:
[B]r <=[/B] [B]16.67[/B]

Blueberries are $4.99 a pound. Diego buys b pounds of blueberries and pays $14.95.

Blueberries are $4.99 a pound. Diego buys b pounds of blueberries and pays $14.95.
Since price * quantity = cost, we have the equation:
4.99b = 14.95
To solve for b, [URL='https://www.mathcelebrity.com/1unk.php?num=4.99b%3D14.95&pl=Solve']we type this equation into our search engine[/URL] and we get:
b = [B]$3.00[/B]

Bob bought 10 note books and 4 pens for 18$. Bill bought 6 notebooks and 4 pens for 12$. Find the pr

Bob bought 10 note books and 4 pens for 18$. Bill bought 6 notebooks and 4 pens for 12$. Find the price of one note book and one pen.
Let the price of each notebook be n. Let the price of each pen be p. We're given two equations:
[LIST=1]
[*]10n + 4p = 18
[*]6n + 4p = 12
[/LIST]
Since we have matching coefficients for p, we subtract equation 1 from equation 2:
(10 - 6)n + (4 - 4)p = 18 - 12
Simplifying and cancelling, we get:
4n = 6
[URL='https://www.mathcelebrity.com/1unk.php?num=4n%3D6&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]n = 1.5[/B]
Now, substitute this value for n into equation (2):
6(1.5) + 4p = 12
Multiply through:
9 + 4p = 12
[URL='https://www.mathcelebrity.com/1unk.php?num=9%2B4p%3D12&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]p = 0.75[/B]

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 fe

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 feet. Use the perimeter formula to find the width of the rectangular yard in inches: P = 2L + 2W.
Plugging our numbers in for P = 22 and L = 5, we get:
22 = 2(5) + 2W
22 = 10 + 2w
Rewritten, we have:
10 + 2w = 22
[URL='https://www.mathcelebrity.com/1unk.php?num=10%2B2w%3D22&pl=Solve']Plug this equation into the search engine[/URL], we get:
[B]w = 6[/B]

Bob finished reading his book in x days. Each day, he read 4 pages. His book has 28 pages

Bob finished reading his book in x days. Each day, he read 4 pages. His book has 28 pages
Our equation for this is found by multiplying pages per day times number of days;
4x = 28
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3D28&pl=Solve']we type the equation into our search engine[/URL] and we get:
x = [B]7[/B]

Bob has half as many quarters as dimes. He has $3.60. How many of each coin does he have?

Bob has half as many quarters as dimes. He has $3.60. How many of each coin does he have?
Let q be the number of quarters. Let d be the number of dimes. We're given:
[LIST=1]
[*]q = 0.5d
[*]0.25q + 0.10d = 3.60
[/LIST]
Substitute (1) into (2):
0.25(0.5d) + 0.10d = 3.60
0.125d + 0.1d = 3.6
Combine like terms:
0.225d = 3.6
[URL='https://www.mathcelebrity.com/1unk.php?num=0.225d%3D3.6&pl=Solve']Typing this equation into our search engine[/URL], we're given:
[B]d = 16[/B]
Substitute d = 16 into Equation (1):
q = 0.5(16)
[B]q = 8[/B]

Bob is twice as old as Henry. The sum of their ages is 42. How old is Henry?

Bob is twice as old as Henry. The sum of their ages is 42. How old is Henry?
Let Bob's age be b. Let Henry's age be h. We're given two equations:
[LIST=1]
[*]b = 2h
[*]b + h = 42
[/LIST]
Substitute b = 2h in equation 1 into equation 2 for b:
2h + h = 42
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2h%2Bh%3D42&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]14[/B]

Brian's age is 3/4 of Marcus'. The sum of their ages is 14. How old are Marcus and Brian?

Brian's age is 3/4 of Marcus'. The sum of their ages is 14. How old are Marcus and Brian?
Let Marcus's age be m.
Then Brian's age = 3/4m
The sum is:
m + 3m/4 = 14
Combine like terms
7m/4 = 14
Cross multiply:
7m = 56
[URL='http://www.mathcelebrity.com/1unk.php?num=7m%3D56&pl=Solve']Plugging this into the search engine[/URL], we get m = 8.
So Brian's age = 3(8)/4 = 24/4 = 6

Bruno is 3x years old and his son is x years old now. Their combined age is 40 years. How old is Bru

Bruno is 3x years old and his son is x years old now. Their combined age is 40 years. How old is Bruno
Combined age means we add, so we have:
3x + x = 40
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x%2Bx%3D40&pl=Solve']type it in our search engine[/URL] and we get:
x = 10
This means Bruno is:
3(10) = [B]30[/B]

Bud makes $400 more per month than maxine If their total income is $3600 how much does bud earn per

Bud makes $400 more per month than maxine If their total income is $3600 how much does bud earn per month
Let Bud's earnings be b.
Let Maxine's earnings be m.
We're given two equations:
[LIST=1]
[*]b = m + 400
[*]b + m = 3600
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for b
m + 400 + m = 3600
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B400%2Bm%3D3600&pl=Solve']type it in our search engine[/URL] and we get:
m = 1600
To solve for b, we substitute m = 1600 into equation (1) above:
b = 1600 + 400
b = [B]2200[/B]

Building A is 150 feet shorter than Building B. The height of both building is 1530 feet. Find the h

Building A is 150 feet shorter than Building B. The height of both building is 1530 feet. Find the height of both building A and B.
Let a be the height of building A
Let b be the height of building B
We're given two equations:
[LIST=1]
[*]a = b - 150
[*]a + b = 1530
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for a:
(b - 150) + b = 1530
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b-150%2Bb%3D1530&pl=Solve']type it in our search engine[/URL] and we get:
b = [B]840[/B]
To solve for a, we substitute b = 840 into equation (1):
a = 840 - 150
a = [B]690[/B]

Caleb has a complicated and difficult research paper due soon. What should he do to keep from feelin

Caleb has a complicated and difficult research paper due soon. What should he do to keep from feeling overwhelmed and procrastinating? A. work on the paper every day but save the bulk of the work for the night before it's due B. break down the paper into several small steps and start with the smallest one C. write down the deadline for the paper where he can see it every day so he doesn't forget D. work on the hardest parts of the paper first and take multiple breaks until he's finished
Caleb wants to avoid both overwhelm and procrastination. Let's review each option:
[LIST]
[*]A is out because saving a majority of the work will cause overwhelm [U]and[/U] demonstrates procrastination
[*]B is a good option as small steps reduce overwhelm
[*]C looks nice on paper, but will he follow through with seeing the deadline everyday?
[*]D is a good option as well. Finishing the tough parts first makes the rest of the journey seem like a downhill cruise
[/LIST]
Based on these, I'd take [B]B or D[/B]

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appr

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations.
Let Cam's age be c. Let Lara's age be l. We're given two equations:
[LIST=1]
[*]c = l + 3 <-- older means we add
[*]c + l = 63 <-- combined ages mean we add
[/LIST]
Substitute equation (1) into equation (2):
l + 3 + l = 63
Combine like terms to simplify our equation:
2l + 3 = 63
To solve for l, [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B3%3D63&pl=Solve']we type this equation into our search engine[/URL] and we get:
l = [B]30[/B]
Now, we plug l = 30 into equation (1) to solve for c:
c = 30 + 3
c = [B]33[/B]

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appr

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations.
Let Cam's age be c.
Let Lara's age be l.
We're given two equations:
[LIST=1]
[*]c = l + 3 (Since older means we add)
[*]c + l = 63
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for c:
l + 3 + l = 63
To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l%2B3%2Bl%3D63&pl=Solve']type it in our search engine [/URL]and we get:
l = [B]30
[/B]
Now, we take l = 30 and substitute it in equation (1) to solve for c:
c = 30 + 3
c = [B]33[/B]

can someone help me with how to work out this word problem?

V = 1/3(pi)r^2h
You want dv/dt. Here is an [URL='https://www.freemathhelp.com/forum/archive/index.php/t-77610.html']example[/URL]:

can someone help me with how to work out this word problem?

Hey there, I'm working for a PapersGram which helps people like you with everything. I'm a researcher by myself but you can try to [URL='https://papersgram.com/assignment-writing-service/']buy assignment[/URL] too. Hope it is helpful.

Cardioid

Shows you the area, arc length, polar equation of the horizontal cardioid, and the polar equation of the vertical cardioid

carlos drank 2,740 ml of water after football practice how many liters did he drink

carlos drank 2,740 ml of water after football practice how many liters did he drink
We [URL='https://www.mathcelebrity.com/liqm.php?quant=2740&pl=Calculate&type=milliliter']type 2740 ml into our search engine[/URL] and we get:
[B]2.74L[/B]

Carly grew 50 plants with 25 seed packets. With 37 seed packets, how many total plants can Carly hav

Carly grew 50 plants with 25 seed packets. With 37 seed packets, how many total plants can Carly have in her backyard? Solve using unit rates.
Set up a proportion of plants per seed packets where p is the number of plants per 37 seed packets.
50/25 = p/37
Copying and pasting this problem [URL='http://www.mathcelebrity.com/prop.php?num1=50&num2=p&den1=25&den2=37&propsign=%3D&pl=Calculate+missing+proportion+value']into our search engine[/URL], we get [B]p = 74[/B].

Cathy wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another

Cathy wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another gym has no joining fee and costs $60 per month. a. In how many months will both gym memberships cost the same? What will that cost be?
Set up cost equations where m is the number of months enrolled:
[LIST=1]
[*]C(m) = 35m + 150
[*]C(m) = 60m
[/LIST]
Set them equal to each other:
35m + 150 = 60m
[URL='http://www.mathcelebrity.com/1unk.php?num=35m%2B150%3D60m&pl=Solve']Pasting the equation above into our search engine[/URL], we get [B]m = 6[/B].

Charmaine’s fish tank has 16 liters of water in it. she plans to add 6 liters per minute until the t

Charmaine’s fish tank has 16 liters of water in it. she plans to add 6 liters per minute until the tank has at least 58 liters. What are the possible numbers of minutes Charmaine could add water?
This is an algebraic inequality. The phrase [I]at least[/I] means greater than or equal to. So we have:
6m + 16 >= 58 <-- This is our algebraic expression/inequality.
To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=6m%2B16%3E%3D58&pl=Solve']we type this into our search engine [/URL]and we get:
[B]m >= 7[/B]

Clara can bake 17 cookies with each scoop of flour. With two scoops of flour, how many cookies can C

Clara can bake 17 cookies with each scoop of flour. With two scoops of flour, how many cookies can Clara bake?
Set up a proportion where x is the number of cookies per 2 scoops of flour
17 cookies/1 scoop = x cookies/2 scoops
[URL='http://www.mathcelebrity.com/prop.php?num1=17&num2=x&den1=1&den2=2&propsign=%3D&pl=Calculate+missing+proportion+value']Running this in the search engine, we get[/URL]:
[B]x = 34 cookies[/B]

Clark wants to give some baseball cards to his friends. If he gives 6 cards to each of his friends,

Clark wants to give some baseball cards to his friends. If he gives 6 cards to each of his friends, he will have 5 cards left. If he gives 8 cards to each of his friends, he will need 7 more cards. How many friends is the giving the cards to?
Let the number of friends Clark gives his cards to be f. Let the total amount of cards he gives out be n. We're given 2 equations:
[LIST=1]
[*]6f + 5 = n
[*]8f - 7 = n
[/LIST]
Since both equations equal n, we set these equations equal to each other
6f + 5 = 8f - 7
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=6f%2B5%3D8f-7&pl=Solve']type this equation into our search engine[/URL] and we get:
f = [B]6
[/B]
To check our work, we plug in f = 6 into each equation:
[LIST=1]
[*]6(6) + 5 = 36 + 5 = 41
[*]8(6) - 7 = 48 - 7 = 41
[/LIST]
So this checks out. Clark has 41 total cards which he gives to 6 friends.

Craig went bowling with $25 to spend. He rented shoes for $5.25 and paid $4.00 for each game. What w

Craig went bowling with $25 to spend. He rented shoes for $5.25 and paid $4.00 for each game. What was the greatest number of games Craig could have played?
Set up the cost function C(g) where g is the number of games Craig plays:
C(g) = Game fee * number of games (g) + shoe rental fee
C(g) = 4g + 5.25
The problem asks for the maximum number of games Craig can play for $25. So we want an inequality of [I]less than or equal to[/I].
4g + 5.25 <= 25
[URL='https://www.mathcelebrity.com/1unk.php?num=4g%2B5.25%3C%3D25&pl=Solve']Type this inequality into our search engine[/URL], and we get:
g <= 4.9375
We want exact games, so we round this down to [B]4 games[/B].

Dakota needs a total of $400 to buy a new bicycle. He has $40 saved. He earns $15 each week deliveri

Dakota needs a total of $400 to buy a new bicycle. He has $40 saved. He earns $15 each week delivering newspapers. How many weeks will Dakota have to deliver papers to have enough money to buy the bicycle?
Let w be the number of weeks of delivering newspapers. We have the equation:
15w + 40 = 400
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=15w%2B40%3D400&pl=Solve']type this equation into our search engine[/URL] and we get:
w = [B]24[/B]

Dan bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of h

Dan bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 26 cards left. How many cards did Dan start with?
Let the starting amount of cards be s. We're given:
[LIST]
[*]Dan bought 7 new cards: s + 7
[*]The dog ate half of his collection. This means he's left with half, or (s + 7)/2
[*]Now, he's got 26 cards left. So we set up the following equation:
[/LIST]
(s + 7)/2 = 26
Cross multiply:
s + 7 = 26 * 2
s + 7 = 52
To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B7%3D52&pl=Solve']we plug this equation into our search engine[/URL] and we get:
s = [B]45[/B]

Dan's school is planning a field trip to an art museum. Bus company A charges a $60 rental fee plus

Dan's school is planning a field trip to an art museum. Bus company A charges a $60 rental fee plus $4 per student. Bus company B charges $150 plus $2 per student. How many students would have to go for the cost to be the same?
[U]Set up Company A's cost equation C(s) where s is the number of students[/U]
C(s) = Cost per student * s + Rental Fee
C(s) = 4s + 60
[U]Set up Company B's cost equation C(s) where s is the number of students[/U]
C(s) = Cost per student * s + Rental Fee
C(s) = 2s + 150
The problem asks for s where both C(s) equations would be equal. So we set Company A and Company B's C(s) equal to each other:
4s + 60 = 2s + 150
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B60%3D2s%2B150&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]45[/B]

Daniel is 41 inches tall. He is 3/5 as tall as his brother. How tall is his brother?

Daniel is 41 inches tall. He is 3/5 as tall as his brother. How tall is his brother?
We set Daniel's brother's height at h. We have:
3h/5 = 41
To solve this equation for h, we [URL='https://www.mathcelebrity.com/prop.php?num1=3h&num2=41&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
[B]h = 68.3333 or 68 & 1/3[/B]

Daniel is 6cm taller than Kamala. If their total height is 368cm, how tall is Kamala?

Daniel is 6cm taller than Kamala. If their total height is 368cm, how tall is Kamala?
Let Daniel's height be d. Let Kamala's height be k. We're given two equations:
[LIST=1]
[*]d = k + 6
[*]d + k = 368
[/LIST]
Substitute equation (1) into equation (2) for d:
k + 6 + k = 368
To solve for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=k%2B6%2Bk%3D368&pl=Solve']type this equation into our search engine[/URL] and we get:
k = [B]181[/B]

David has b dollars in his bank account; Claire has three times as much money as David. The sum of t

David has b dollars in his bank account; Claire has three times as much money as David. The sum of their money is $240. How much money does Claire have?
David has b
Claire has 3b since three times as much means we multiply b by 3
The sum of their money is found by adding David's bank balance to Claire's bank balance to get the equation:
3b + b = 240
To solve for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b%2Bb%3D240&pl=Solve']we type this equation into our search engine[/URL] and we get:
b = 60
So David has 60 dollars in his bank account.
Therefore, Claire has:
3(60) = [B]180[/B]

Debbie baked 32 cookies with 4 scoops of flour. With 10 scoops of flour, how many cookies can Debbie

Debbie baked 32 cookies with 4 scoops of flour. With 10 scoops of flour, how many cookies can Debbie bake?
Set up a proportion of cookies to scoops of flour, where c is the number of cookies per 10 scoops of flour:
32/4 = c/10
[URL='https://www.mathcelebrity.com/prop.php?num1=32&num2=c&den1=4&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
c = [B]80[/B]

Dedra took a total of 6 pages of notes during 2 hours of class. After attending 3 hours of class, ho

Dedra took a total of 6 pages of notes during 2 hours of class. After attending 3 hours of class, how many total pages of notes will Dedra have in her notebook?
Set up a proportion of pages of notes to hours of class where p equals the number of pages of notes Dedra takes for 3 hours of class:
6/2 = p/3
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=p&den1=2&den2=3&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
p = [B]9[/B]

devaughn,sageis2timessydneysage,thesumoftheiragesis78,whatissydneysage

devaughn,sageis2timessydneysage,thesumoftheiragesis78,whatissydneysage
Let d be Devaughn's age. Let s be Sydney's age. We have two equations:
[LIST=1]
[*]d = 2s
[*]d + s = 78
[/LIST]
Substitute (1) into (2)
2s + s = 78
3s = 78
Entering [URL='http://www.mathcelebrity.com/1unk.php?num=3s%3D78&pl=Solve']3x = 78 into the search engine[/URL], we get [B]s = 26[/B].

Deyjiana reads 30 pages in 25 minutes. If she reads 210 pages at this rate, how long will it take he

Deyjiana reads 30 pages in 25 minutes. If she reads 210 pages at this rate, how long will it take her?
Set up a proportion of pages to minutes, were m is the number of minutes it takes to read 210 pages:
30/25 = 210/m
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=30&num2=210&den1=25&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search engine[/URL] and we get:
m = [B]175[/B]

Dina is twice as old as Andrea. The sum of their age is 72. Find their present ages.

Dina is twice as old as Andrea. The sum of their age is 72. Find their present ages.
Let d be Dina's age. Let a be Andrea's age. We're given:
[LIST=1]
[*]d = 2a <-- Twice means multiply by 2
[*]a + d = 72
[/LIST]
Substitute equation (1) into equation (2):
a + 2a = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=a%2B2a%3D72&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]a = 24[/B]
Substitute a = 24 into equation (1):
d = 2(24)
[B]d = 48
So Andrea is 24 years old and Dina is 48 years old[/B]

Dinh has 4 more patients to care for than Juan. if Dinah has 18 patients to care for how many does J

Dinh has 4 more patients to care for than Juan. if Dinah has 18 patients to care for how many does Juan?
Let d = j + 14.
Since d = 18, we have:
18 = j + 14
[URL='http://www.mathcelebrity.com/1unk.php?num=j%2B14%3D18&pl=Solve']Plug this into the search engine and we have[/URL]
j = 4

Divide 73 into two parts whose product is 402

Divide 73 into two parts whose product is 40
Our first part is x
Our second part is 73 - x
The product of the two parts is:
x(73 - x) = 40
Multiplying through, we get:
-x^2 + 73x = 402
Subtract 40 from each side, we get:
-x^2 + 73x - 402 = 0
This is a quadratic equation. To solve this, we type it in our search engine, choose "solve Quadratic", and we get:
[LIST=1]
[*]x = [B]6[/B]
[*]x = [B]67[/B]
[/LIST]

Dora has $35 saved. She earns $9.50 per hour at her job. How many hours must she work to have a tota

Dora has $35 saved. She earns $9.50 per hour at her job. How many hours must she work to have a total of $358 in her savings?
Subtract the existing savings from the desired savings to see what we have left:
358 - 35 = 323
Now, at 9.50 per hour, how many hours of work does she need to get 323?
Let h be the number of hours. We have:
9.50h = 323
[URL='http://www.mathcelebrity.com/1unk.php?num=9.50h%3D323&pl=Solve']Running this problem through our search engine[/URL], we get
[B]h = 34[/B]

DoubleClick Search Fundamentals

Exam answers and study guide for the Google DoubleClick Search Fundamentals exam

Dylan is playing darts. He hit the bullseye on 5 out of his last 20 tosses. Considering this data, h

Dylan is playing darts. He hit the bullseye on 5 out of his last 20 tosses. Considering this data, how many bullseyes would you expect Dylan to get during his next 16 tosses?
We have a proportion of bullseyes to tosses where b is the number of bullseyes for 16 tosses:
5/20 = b/16
[URL='https://www.mathcelebrity.com/prop.php?num1=5&num2=b&den1=20&den2=16&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get:
b = [B]4[/B]

each classroom at HCS has a total of 26 desks. After Mr. Sean pond ordered 75 new desks the total nu

each classroom at HCS has a total of 26 desks. After Mr. Sean pond ordered 75 new desks the total number of desks in the school was 543. How many classrooms does the school have?
Let d be the number of desks per classroom. We're given an equation:
26d + 75 = 543
To solve for d, [URL='https://www.mathcelebrity.com/1unk.php?num=26d%2B75%3D543&pl=Solve']type this equation into our search engine[/URL] and we get:
d = [B]18[/B]

Each of letters in the word PROPER are on separate cards, face down on the table. If you pick a card

Each of letters in the word PROPER are on separate cards, face down on the table. If you pick a card at random, what is the probability that its letter will be P or R?
PROPER has 6 letters in it. It has 2 P's and 2 R's. So we have:
Pr(P or R) = Pr(P) + Pr(R)
Pr(P or R) = 2/6 + 2/6
Pr(P or R) = 4/6
We can simplify this. So [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F6&frac2=3%2F8&pl=Simplify']we type this fraction in our search engine[/URL], choose simplify, and we get:
Pr(P or R) = [B]2/3[/B]

Each piece of candy costs 25 cents. The cost of x pieces of candy is $2.00. Use variable x to transl

Each piece of candy costs 25 cents. The cost of x pieces of candy is $2.00. Use variable x to translate the above statements into algebraic equation.
Our algebraic expression is:
[B]0.25x = 2
[/B]
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.25x%3D2&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]8[/B]

eight oranges are $1.00 how much would 5 dozen oranges cost?

eight oranges are $1.00 how much would 5 dozen oranges cost?
Set up a proportion of oranges to cost where c is the cost for 5 dozen = 60 oranges:
8/1 = 60/c
To solve this proportion, [URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=60&den1=1&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
c = [B]7.5[/B]

Elsa took a total of 25 quizzes over the course of 5 weeks. After attending 8 weeks of school this q

Elsa took a total of 25 quizzes over the course of 5 weeks. After attending 8 weeks of school this quarter, how many quizzes will Elsa have taken in total? Assume the relationship is directly proportional.
Set up a proportion of quizzes to weeks where q is the number of quizzes taken in 8 weeks. We have:
25/5 = q/8
We [URL='https://www.mathcelebrity.com/prop.php?num1=25&num2=q&den1=5&den2=8&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search engine[/URL] and we get:
q = [B]40[/B]

eric is twice as old as Shawn. The sum of their ages is 33. How old is Shawn?

eric is twice as old as Shawn. The sum of their ages is 33. How old is Shawn?
Let Eric's age be e. Let Shawn's age be s. We're given two equations:
[LIST=1]
[*]e = 2s
[*]e + s = 33
[/LIST]
Substitute equation (1) into equation (2) for e so we can solve for s:
2s + s = 33
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=2s%2Bs%3D33&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]11[/B]

Ethan has $9079 in his retirement account, and Kurt has $9259 in his. Ethan is adding $19per day, wh

Ethan has $9079 in his retirement account, and Kurt has $9259 in his. Ethan is adding $19per day, whereas Kurt is contributing $1 per day. Eventually, the two accounts will contain the same amount. What balance will each account have? How long will that take?
Set up account equations A(d) where d is the number of days since time 0 for each account.
Ethan A(d): 9079 + 19d
Kurt A(d): 9259 + d
The problems asks for when they are equal, and how much money they have in them. So set each account equation equal to each other:
9079 + 19d = 9259 + d
[URL='https://www.mathcelebrity.com/1unk.php?num=9079%2B19d%3D9259%2Bd&pl=Solve']Typing this equation into our search engine[/URL], we get [B]d = 10[/B].
So in 10 days, both accounts will have equal amounts in them.
Now, pick one of the account equations, either Ethan or Kurt, and plug in d = 10. Let's choose Kurt's since we have a simpler equation:
A(10) = 9259 + 10
A(10) = $[B]9,269
[/B]
After 10 days, both accounts have $9,269 in them.

Euclidean Geometry

Shows you the area, arc length, polar equation of the horizontal cardioid, and the polar equation of the vertical cardioid

Excel Formula Tutorial

This is a downloadable interactive excel file tutorial showing you functions in Excel with examples.

It allows you to change input in blue, and the tutorial notes will dynamically update so that you can learn fast.

Also contains an instant search box that will return excel function information immediately as you type

It allows you to change input in blue, and the tutorial notes will dynamically update so that you can learn fast.

Also contains an instant search box that will return excel function information immediately as you type

Factors of 36 between 2 and 12

Factors of 36 between 2 and 12
We type in [I][URL='https://www.mathcelebrity.com/factoriz.php?num=36&pl=Show+Factorization']factors of 36[/URL][/I] into our search engine and we get:
{1, 2, 3, 4, 6, 9, 12, 18, 36}
The problem asks for factors of 36 between 2 and 12:
Between does not mean inclusive, so we have anything greater than 2 and less than 12:
[B]{3, 4, 6, 9}[/B]

Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith?

Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith?
Let Faith's age be f. Let her mother's age be m. We're given:
[LIST=1]
[*]f = m/5
[*]f + m = 30
[/LIST]
Rearrange (1) by cross-multiplying:
m = 5f
Substitute this into equation (2):
f + 5f = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=f%2B5f%3D30&pl=Solve']Type this equation into our search engine[/URL] and we get:
f = [B]5[/B]

Farmer Bob can get 10 gallons of milk from 4 cows. How many gallons of milk can he get from 14 cows?

Farmer Bob can get 10 gallons of milk from 4 cows. How many gallons of milk can he get from 14 cows?
Set up a proportion of gallons to cows where g is the number of gallons per 14 cows:
10/4 = g/14
To solve this proportion for g, we[URL='https://www.mathcelebrity.com/prop.php?num1=10&num2=g&den1=4&den2=14&propsign=%3D&pl=Calculate+missing+proportion+value'] type it in our search engine[/URL] and we get:
g = [B]35
[/B]

Farmer Yumi has too many plants in her garden. If she starts out with 150 plants and is losing them

Farmer Yumi has too many plants in her garden. If she starts out with 150 plants and is losing them at a rate of 4% each day, how long will it take for her to have 20 plants left? Round UP to the nearest day.
We set up the function P(d) where d is the number of days sine she started losing plants:
P(d) = Initial plants * (1 - Loss percent / 100)^d
Plugging in our numbers, we get:
20 = 150 * (1 - 4/100)^d
20 = 150 * (1 - 0.04)^d
Read left to right so it's easier to read:
150 * 0.96^d = 20
Divide each side by 150, and we get:
0.96^d = 0.13333333333
To solve this logarithmic equation for d, we [URL='https://www.mathcelebrity.com/natlog.php?num=0.96%5Ed%3D0.13333333333&pl=Calculate']type it in our search engine[/URL] and we get:
d = 49.35
The problem tells us to round up, so we round up to [B]50 days[/B]

Find 2 consecutive numbers such that the sum of twice the smaller number and 3 times the larger numb

Find 2 consecutive numbers such that the sum of twice the smaller number and 3 times the larger number is 73.
Let x be the smaller number and y be the larger number. We are given:
2x + 3y = 73
Since the numbers are consecutive, we know that y = x + 1. Substitute this into our given equation:
2x + 3(x + 1) = 73
Multiply through:
2x + 3x + 3 = 73
Group like terms:
5x + 3 = 73
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3%3D73&pl=Solve']Type 5x + 3 = 73 into the search engine[/URL], and we get [B]x = 14[/B].
Our larger number is 14 + 1 = [B]15
[/B]
Therefore, our consecutive numbers are[B] (14, 15)[/B]

Find Necessary Sample Size

The monthly earnings of a group of business students are are normally distributed with a standard deviation of 545 dollars. A researcher wants to estimate the mean monthly earnings of all business students. Find the sample size needed to have a confidence level of 95% and a margin of error of 128 dollars.

Find r in P(7, r)

Find r in P(7, r)
Recall the permutations formula:
7! / (7-r!) = 840.
We [URL='https://www.mathcelebrity.com/factorial.php?num=7!&pl=Calculate+factorial']run 7! through our search engine[/URL] and we get:
[URL='https://www.mathcelebrity.com/factorial.php?num=7!&pl=Calculate+factorial']7![/URL] = 5040
5040 / (7 - r)! = 840
Cross multiply, and we get:
5040/840 = 7 - r!
6 = (7 - r)!
Since 6 = 3*2*! = 3!, we have;
3! = (7 - r)!
3 = 7 - r
To solve for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=3%3D7-r&pl=Solve']type this equation into our search engine[/URL] and we get:
r = [B]4[/B]

Find Requested Value

Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, in liters.
5.2 4.9 2.9 5.3 3.0
4.0 5.2 5.2 3.2 4.7
3.2 3.5 4.8 4.0 5.1
Use the data to obtain a point estimate of the mean forced vital capacity for all asthmatics

Find the confidence interval specified.

Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, in liters.
5.1 4.9 4.7 3.1 4.3
3.7 3.7 4.3 3.5 5.2
3.2 3.5 4.8 4.0 5.1
Use the data to obtain a 95.44% confidence interval for the mean forced vital capacity for all asthmatics. Assume that ? = 0.7.

Find the explicit formula of the sequence 3,12,48

Find the explicit formula of the sequence 3,12,48
We [URL='https://www.mathcelebrity.com/sequenceag.php?num=3,12,48&n=10&pl=Calculate+Series']type in 3,12,48 into our search engine[/URL]. Choose series, and we get:
[B]a(n) = 3 * 4^(n - 1)[/B]

Find the gradient of the the line with the equation 8x - 4y =12

Find the gradient of the the line with the equation 8x - 4y =12
[URL='https://www.mathcelebrity.com/parperp.php?line1=8x-4y%3D12&line2=6x+-+3y+%3D+18&pl=Slope']Type this equation into our search engine[/URL] and choose "slope" and we get:
Slope (gradient) = [B]2[/B]

Find the greatest number which divides 845 and 1250

Find the greatest number which divides 845 and 1250
This is the greatest common factor. We [URL='https://www.mathcelebrity.com/gcflcm.php?num1=845&num2=1250&num3=&pl=GCF+and+LCM']type GCF(845,1250) into our search engine [/URL]and we get:
[B]5[/B]

Find the largest of three consecutive even integers when six times the first integers is equal to fi

Find the largest of three consecutive even integers when six times the first integers is equal to five times the middle integer.
Let the first of the 3 consecutive even integers be n.
The second consecutive even integer is n + 2.
The third (largest) consecutive even integer is n + 4.
We are given 6n = 5(n + 2).
Multiply through on the right side, and we get:
6n = 5n + 10
[URL='https://www.mathcelebrity.com/1unk.php?num=6n%3D5n%2B10&pl=Solve']Typing 6n = 5n + 10 into the search engine[/URL], we get n = 10.
Remember, n was our smallest of 3 consecutive even integers. So the largest is:
n + 4
10 + 4
[B]14[/B]

Find the midpoint of the set of points (4,4) and (0,6)

Find the midpoint of the set of points (4,4) and (0,6)
We [URL='https://www.mathcelebrity.com/slope.php?xone=4&yone=4&slope=+2%2F5&xtwo=0&ytwo=6&pl=You+entered+2+points']type in (4,4) and (0,6) into our search engine [/URL]and we get:
Midpoint = [B](2, 5)[/B]

Find two consecutive integers if the sum of their squares is 1513

Find two consecutive integers if the sum of their squares is 1513
Let the first integer be n. The next consecutive integer is (n + 1).
The sum of their squares is:
n^2 + (n + 1)^2 = 1513
n^2 + n^2 + 2n + 1 = 1513
2n^2 + 2n + 1 = 1513
Subtract 1513 from each side:
2n^2 + 2n - 1512 = 0
We have a quadratic equation. We [URL='https://www.mathcelebrity.com/quadratic.php?num=2n%5E2%2B2n-1512%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type this into our search engine[/URL] and get:
n = (-27, 28)
Let's take the positive solution.
The second integer is: n + 1
28 + 1 = 29

Find two consecutive odd integers such that the sum of their squares is 290

Find two consecutive odd integers such that the sum of their squares is 290.
Let the first odd integer be n.
The next odd integer is n + 2
Square them both:
n^2
(n + 2)^2 = n^2 + 4n + 4 from our [URL='https://www.mathcelebrity.com/expand.php?term1=%28n%2B2%29%5E2&pl=Expand']expansion calculator[/URL]
The sum of the squares equals 290
n^2 + n^2 + 4n + 4 = 290
Group like terms:
2n^2 + 4n + 4 = 290
[URL='https://www.mathcelebrity.com/quadratic.php?num=2n%5E2%2B4n%2B4%3D290&pl=Solve+Quadratic+Equation&hintnum=+0']Enter this quadratic into our search engine[/URL], and we get:
n = 11, n = -13
Which means the two consecutive odd integer are:
11 and 11 + 2 = 13. [B](11, 13)[/B]
-13 and -13 + 2 = -11 [B](-13, -11)[/B]

Find two consecutive positive integers such that the difference of their square is 25

Find two consecutive positive integers such that the difference of their square is 25.
Let the first integer be n. This means the next integer is (n + 1).
Square n: n^2
Square the next consecutive integer: (n + 1)^2 = n^2 + 2n + 1
Now, we take the difference of their squares and set it equal to 25:
(n^2 + 2n + 1) - n^2 = 25
Cancelling the n^2, we get:
2n + 1 = 25
[URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B1%3D25&pl=Solve']Typing this equation into our search engine[/URL], we get:
n = [B]12[/B]

Find y if the line through (1, y) and (2, 7) has a slope of 4.

Find y if the line through (1, y) and (2, 7) has a slope of 4.
Given two points (x1, y1) and (x2, y2), Slope formula is:
slope = (y2 - y1)/(x2 - x1)
Plugging in our coordinates and slope to this formula, we get:
(7 - y)/(2 - 1) = 4
7 - y/1 = 4
7 - y = 4
To solve this equation for y, w[URL='https://www.mathcelebrity.com/1unk.php?num=7-y%3D4&pl=Solve']e type it in our search engine[/URL] and we get:
y = [B]3[/B]

Five one -foot rulers laid end to end reach how many inches?

Five one -foot rulers laid end to end reach how many inches?
Since [URL='https://www.mathcelebrity.com/linearcon.php?quant=5&pl=Calculate&type=foot']1 foot = 12 inches from our conversion calculator[/URL], we have:
5 feet = [B]60 inches[/B]

Five times Kim's age plus 13 equals 58. How old is Kim?

Five times Kim's age plus 13 equals 58. How old is Kim?
Let Kim's age be a. We have:
Five times Kim's age:
5a
Plus 13 means we add 13
5a + 13
Equals 58 means we set the expression 5a + 13 equal to 58
5a + 13 = 58 <-- This is our algebraic expression
To solve this equation for a, [URL='https://www.mathcelebrity.com/1unk.php?num=5a%2B13%3D58&pl=Solve']we type it into our search engine[/URL] and get:
a = [B]9[/B]

For g(x) = 4-5x, determine the input for x when the output of g(x) is -6

For g(x) = 4-5x, determine the input for x when the output of g(x) is -6
We want to know when:
4 - 5x = 6
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=4-5x%3D6&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]-0.4 or -2/5[/B]

For her phone service, Maya pays a monthly fee of $27 , and she pays an additional $0.04 per minu

For her phone service, Maya pays a monthly fee of $27 , and she pays an additional $0.04 per minute of use. The least she has been charged in a month is $86.04 . What are the possible numbers of minutes she has used her phone in a month? Use m for the number of minutes, and solve your inequality for m .
Maya's cost function is C(m), where m is the number of minutes used.
C(m) = 0.04m + 27
We are given C(m) = $86.04. We want her cost function [I]less than or equal[/I] to this.
0.04m + 27 <= 86.04
[URL='https://www.mathcelebrity.com/1unk.php?num=0.04m%2B27%3C%3D86.04&pl=Solve']Type this inequality into our search engine[/URL], and we get [B]m <= 1476[/B].

for the function, h(x) = bx - 22, b is a constant and h(-5) = -7. Find the value of h(5)

for the function, h(x) = bx - 22, b is a constant and h(-5) = -7. Find the value of h(5)
h(-5) = -5b - 22
Since we're given h(-5) = -7, we have:
-5b - 22 = -7
[URL='https://www.mathcelebrity.com/1unk.php?num=-5b-22%3D-7&pl=Solve']Typing this equation into our search engine[/URL], we get:
b = -3
So our h(x) equation is now:
h(x) = -3x - 22
The problem asks for h(5):
h(5) = -3(5) - 22
h(5) = 15 - 22
h(5) = [B]-37[/B]

Fortran Function Tutorial

A Search Engine with definitions on Fortran functions

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?
So the last cousin is n years old. this means consecutive cousins are n + 2 years older than the next.
whether their ages are even or odd, we have the sum of 4 consecutive (odd|even) integers equal to 36. We [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof4consecutiveevenintegersis36&pl=Calculate']type this into our search engine[/URL] and we get the ages of:
[B]6, 8, 10, 12[/B]

Four-fifths of Kayla’s Math Notebook is filled. She has written on 48 pages. How many pages is there

Four-fifths of Kayla’s Math Notebook is filled. She has written on 48 pages. How many pages is there total in the notebook?
Let the total pages be p. WE're given:
4p/5 = 48
To solve for p, we[URL='https://www.mathcelebrity.com/prop.php?num1=4p&num2=48&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value'] type this equation into our search engine[/URL] and we get:
p = [B]60[/B]

From 9 names on a ballot, a committee of 4 will be elected to attend a political national convention

From 9 names on a ballot, a committee of 4 will be elected to attend a political national convention. How many different committees are possible?
We want unique combinations, so we have 9 choose 4, or 9C4.
[URL='https://www.mathcelebrity.com/permutation.php?num=9&den=4&pl=Combinations']Typing this into the search engine[/URL], we get:
9C4 = [B]126 different committees[/B]

From a group of 10 men and 8 women, how many ways can 2 men and 3 women be chosen for 5 positions

From a group of 10 men and 8 women, how many ways can 2 men and 3 women be chosen for 5 positions?
We use combinations. Since men and women are independent, we multiply each result:
We want 10 men choose 2 men multiplied by 8 women choose 3 women.
[URL='https://www.mathcelebrity.com/permutation.php?num=10&den=2&pl=Combinations']Type 10C2 into our search engine[/URL] and we get 45
[URL='https://www.mathcelebrity.com/permutation.php?num=8&den=3&pl=Combinations']Type 8C3 into our search engine[/URL] and we get 56
Multiply both together:
45 * 56 = [B]2,520 ways[/B]

Gabe rents a piano for $49 per month. He earns $15 per hour giving piano lessons to students. How ma

Gabe rents a piano for $49 per month. He earns $15 per hour giving piano lessons to students. How many hours of lessons per month must he give to earn a profit of $326?
Build a profit function P(h) where h is the number of hours:
P(h) = Hourly Rate * Number of Hours (h) - Cost of Piano
P(h) = 15h - 49
The problem asks for the number of hours where P(h) = $326
15h - 49 = 326
We take this equation and [URL='https://www.mathcelebrity.com/1unk.php?num=15h-49%3D326&pl=Solve']type it in our search engine[/URL] to solve for h:
h = [B]25[/B]

Gary is buying chips. Each bag costs $3.50. He has $40 to spend. Write an inequality to represent th

Gary is buying chips. Each bag costs $3.50. He has $40 to spend. Write an inequality to represent the number of chip bags, c, he can afford.
Gary's spend is found by this inequality:
[B]3.50c <= 40
[/B]
To solve this inequality, [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3.50c%3C%3D40&pl=Show+Interval+Notation']we type it in our search engine[/URL] and we get:
[B]c <= 11.43[/B]

George has a certain number of apples, and Sarah has 4 times as many apples as George. They have a t

George has a certain number of apples, and Sarah has 4 times as many apples as George. They have a total of 25 apples.
Let George's apples be g. Let Sarah's apples be s. We're give two equations:
[LIST=1]
[*]s = 4g
[*]g + s = 25
[/LIST]
Substitute equation (1) into equation (2) for s:
g + 4g = 25
If [URL='https://www.mathcelebrity.com/1unk.php?num=g%2B4g%3D25&pl=Solve']we plug this equation into our search engine[/URL] and solve for g, we get:
g = [B]5[/B]
Now substitute this into equation 1 for g = 5:
s = 4(5)
s = [B]20[/B]
[B]So George has 5 apples and Sarah has 20 apples[/B]

Germany and Austria have a total of 25 states. Germany has 7 more states than Austria has. Create 2

Germany and Austria have a total of 25 states. Germany has 7 more states than Austria has. Create 2 equations.
Let g be the number of German states. Let a be the number of Austrian states. We're given two equations:
[LIST=1]
[*]a + g = 25
[*]g = a + 7
[/LIST]
To solve this system of equations, we substitute equation (2) into equation (1) for g:
a + (a + 7) = 25
Combine like terms:
2a + 7 = 25
To solve for a, we[URL='https://www.mathcelebrity.com/1unk.php?num=2a%2B7%3D25&pl=Solve'] type this equation into our search engine[/URL] and we get:
[B]a = 9[/B]
To solve for g, we plug in a = 9 into equation (2):
g = 9 + 7
[B]g = 16[/B]

Giovanni is thinking of a number. If he adds 2 to it, then divides that sum by 3, he gets 7. What is

Giovanni is thinking of a number. If he adds 2 to it, then divides that sum by 3, he gets 7. What is the number?
Let the number be n:
[LIST]
[*]n
[*]Add 2: n + 2
[*]Divide the sum by 3: (n + 2)/3
[*]The word "gets" means an equation, so we set (n + 2)/3 equal to 7
[/LIST]
(n + 2)/3 = 7
Cross multiply:
n + 2 = 21
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B2%3D21&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]19[/B]

Given f = cd^3, f = 450, and d = 10, what is c?

Given f = cd^3, f = 450, and d = 10, what is c?
A) 0.5
B) 4.5
C) 15
D) 45
E) 150
Plugging in our numbers, we get:
c(10)^3 = 450
Since 10^3 = 1000, we have:
1000c = 450
[URL='https://www.mathcelebrity.com/1unk.php?num=1000c%3D450&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]c = 0.45 Answer B[/B]

Given g(x)=-x-1, solve for x when g(x)=3

Given g(x)=-x-1, solve for x when g(x)=3
we have:
-x - 1 = 3
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=-x-1%3D3&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]-4[/B]

Given the function f(x)=3x?9, what is the value of x when f(x)=9

Given the function f(x)=3x?9, what is the value of x when f(x)=9
Plug in our numbers and we get:
3x - 9 = 9
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-9%3D9&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]6[/B]

Google AdWords Advanced Search Exam

Exam answers and study guide for Google AdWords Advanced Search Exam

Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute.Max is hiking a

Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute.Max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute. How many minutes will it take until they're at the same altitude?
Set up the Altitude function A(m) where m is the number of minutes that went by since now.
Set up Graham's altitude function A(m):
A(m) = 14040 - 50m <-- we subtract for descending
Set up Max's altitude function A(m):
A(m) = 12500 + 20m <-- we add for ascending
Set the altitudes equal to each other to solve for m:
14040 - 50m = 12500 + 20m
[URL='https://www.mathcelebrity.com/1unk.php?num=14040-50m%3D12500%2B20m&pl=Solve']We type this equation into our search engine to solve for m[/URL] and we get:
m = [B]22[/B]

Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older tha

Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older than her daughter, but 31 years younger than her mother (the grandmother). How old are the three
Let grandmother's age be g. Let mother's age be m. Let daughter's age be d. We're given 3 equations:
[LIST=1]
[*]m = d + 25
[*]m = g - 31
[*]d + g + m = 150
[/LIST]
This means the daughter is:
d = 25 + 31 = 56 years younger than her grandmother. So we have:
4. d = g - 56
Plugging in equation (2) and equation(4) into equation (3) we get:
g - 56 + g + g - 31
Combine like terms:
3g - 87 = 150
[URL='https://www.mathcelebrity.com/1unk.php?num=3g-87%3D150&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]g = 79[/B]
Plug this into equation (2):
m = 79 - 31
[B]m = 48[/B]
Plug this into equation (4):
d = 79 - 56
[B]d = 23[/B]

Grayson took a total of 16 quizzes over the course of 8 weeks. How many weeks of school will Grayson

Grayson took a total of 16 quizzes over the course of 8 weeks. How many weeks of school will Grayson have to attend this quarter before he will have taken a total of 20 quizzes? Assume the relationship is directly proportional.
Set up a proportion of quizzes to weeks, where w is the number of weeks for 20 quizzes:
16/8 = 20/w
[URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=20&den1=8&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
w = [B]10[/B]

Greg runs 120 m in 20 seconds. How far can he run in one minute?

Greg runs 120 m in 20 seconds. How far can he run in one minute?
We want to compare seconds to seconds.
[URL='https://www.mathcelebrity.com/timecon.php?quant=1&pl=Calculate&type=minute']1 minute[/URL] = 60 seconds
Set up a proportion of meters to seconds where m is the meters ran in 60 seconds:
120/20 = m/60
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=120&num2=m&den1=20&den2=60&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
m. = [B]360 meters[/B]

Guadalupe left the restaurant traveling 12 mph. Then, 3 hours later, Lauren left traveling the same

Guadalupe left the restaurant traveling 12 mph. Then, 3 hours later, Lauren left traveling the same direction at 24 mph. How long will Lauren travel before catching up with Guadalupe?
Distance = Rate x Time
Guadulupe will meet Lauren at the following distance:
12t = 24(t - 3)
12t = 24t - 72
[URL='https://www.mathcelebrity.com/1unk.php?num=12t%3D24t-72&pl=Solve']Typing that equation into our search engine[/URL], we get:
t = 6

Gym A: $75 joining fee and $35 monthly charge. Gym B: No joining fee and $60 monthly charge. (Think

Gym A: $75 joining fee and $35 monthly charge. Gym B: No joining fee and $60 monthly charge. (Think of the monthly charges paid at the end of the month.) Enter the number of months it will take for the total cost for both gyms to be equal.
Gym A cost function C(m) where m is the number of months:
C(m) = Monthly charge * months + Joining Fee
C(m) = 35m + 75
Gym B cost function C(m) where m is the number of months:
C(m) = Monthly charge * months + Joining Fee
C(m) = 60m
Set them equal to each other:
35m + 75 = 60m
To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=35m%2B75%3D60m&pl=Solve']we type this equation into our search engine[/URL] and get:
m = [B]3[/B]

harley had $500 in his bank account at the beginning of the year. he spends $20 each week on food, c

harley had $500 in his bank account at the beginning of the year. he spends $20 each week on food, clothing, and movie tickets. he wants to have more than $100 at the end of summer to make sure he has enough to purchase some new shoes before school starts. how many weeks, w, can harley withdraw money from his savings account and still have more than $100 to buy new shoes?
Let the number of weeks be w. Harley needs $100 (or more) for shoes. We have the balance in Harley's account as:
500 - 20w >= 100
To solve this inequality for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=500-20w%3E%3D100&pl=Solve']type it in our search engine[/URL] and we get:
[B]w <= 20[/B]

Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she took

Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she took four tests. She scored 10 points better on the second test than she did on the first, 20 points better on the third test than on the first, and 30 points better on the fourth test than on the first. If the mean of these four tests was 70, what was her score on the third test?
Givens:
[LIST]
[*]Let the first test score be s:
[*]The second test score is: s + 10
[*]The third test score is: s + 20
[*]The fourth test score is: s + 30
[/LIST]
The mean of the four tests is 70, found below:
Sum of test scores / Number of Tests = Mean
Plugging in our number, we get:
(s + s + 10 + s + 20 + s + 30) / 4 = 70
Cross multiply and simplify:
4s + 60 = 70 * 4
4s + 60 = 280
To [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B60%3D280&pl=Solve']solve this equation for s, we type it in our search engine[/URL] and we get:
s = 55
So the third test score:
s + 20 = 55 + 20
[B]75[/B]

Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts,

Practical Explanation ( For Example ) :- `1st of all can you tell me every single seconds detail from that time when you born ?? ( i need every seconds detail ?? that what- what you have thought and done on every single second )
can you tell me every single detail of your `1 cheapest Minute Or your whole hour, day, week, month, year or your whole life ??
if you are not able to tell me about this life then what proof do you have that you didn't forget your past ? and that you will not forget this present life in the future ?
that is Fact that Supreme Lord Krishna exists but we posses no such intelligence to understand him.
there is also next life. and i already proved you that no scientist, no politician, no so-called intelligent man in this world is able to understand this Truth. cuz they are imagining. and you cannot imagine what is god, who is god, what is after life etc.
_______
for example :Your father existed before your birth. you cannot say that before your birth your father don,t exists.
So you have to ask from mother, "Who is my father?" And if she says, "This gentleman is your father," then it is all right. It is easy.
Otherwise, if you makes research, "Who is my father?" go on searching for life; you'll never find your father.
( now maybe...maybe you will say that i will search my father from D.N.A, or i will prove it by photo's, or many other thing's which i will get from my mother and prove it that who is my Real father.{ So you have to believe the authority. who is that authority ? she is your mother. you cannot claim of any photo's, D.N.A or many other things without authority ( or ur mother ).
if you will show D.N.A, photo's, and many other proofs from other women then your mother. then what is use of those proofs ??} )
same you have to follow real authority. "Whatever You have spoken, I accept it," Then there is no difficulty. And You are accepted by Devala, Narada, Vyasa, and You are speaking Yourself, and later on, all the acaryas have accepted. Then I'll follow.
I'll have to follow great personalities. The same reason mother says, this gentleman is my father. That's all. Finish business. Where is the necessity of making research? All authorities accept Krsna, the Supreme Personality of Godhead. You accept it; then your searching after God is finished.
Why should you waste your time?
_______
all that is you need is to hear from authority ( same like mother ). and i heard this truth from authority " Srila Prabhupada " he is my spiritual master.
im not talking these all things from my own.
___________
in this world no `1 can be Peace full. this is all along Fact.
cuz we all are suffering in this world 4 Problems which are Disease, Old age, Death, and Birth after Birth.
tell me are you really happy ?? you can,t be happy if you will ignore these 4 main problem. then still you will be Forced by Nature.
___________________
if you really want to be happy then follow these 6 Things which are No illicit s.ex, No g.ambling, No d.rugs ( No tea & coffee ), No meat-eating ( No onion & garlic's )
5th thing is whatever you eat `1st offer it to Supreme Lord Krishna. ( if you know it what is Guru parama-para then offer them food not direct Supreme Lord Krishna )
and 6th " Main Thing " is you have to Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare ".
_______________________________
If your not able to follow these 4 things no illicit s.ex, no g.ambling, no d.rugs, no meat-eating then don,t worry but chanting of this holy name ( Hare Krishna Maha-Mantra ) is very-very and very important.
Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare " and be happy.
if you still don,t believe on me then chant any other name for 5 Min's and chant this holy name for 5 Min's and you will see effect. i promise you it works And chanting at least 16 rounds ( each round of 108 beads ) of the Hare Krishna maha-mantra daily.
____________
Here is no Question of Holy Books quotes, Personal Experiences, Faith or Belief. i accept that Sometimes Faith is also Blind. Here is already Practical explanation which already proved that every`1 else in this world is nothing more then Busy Foolish and totally idiot.
_________________________
Source(s):
every `1 is already Blind in this world and if you will follow another Blind then you both will fall in hole. so try to follow that person who have Spiritual Eyes who can Guide you on Actual Right Path. ( my Authority & Guide is my Spiritual Master " Srila Prabhupada " )
_____________
if you want to see Actual Purpose of human life then see this link : ( triple w ( d . o . t ) asitis ( d . o . t ) c . o . m {Bookmark it })
read it complete. ( i promise only readers of this book that they { he/she } will get every single answer which they want to know about why im in this material world, who im, what will happen after this life, what is best thing which will make Human Life Perfect, and what is perfection of Human Life. ) purpose of human life is not to live like animal cuz every`1 at present time doing 4 thing which are sleeping, eating, s.ex & fear. purpose of human life is to become freed from Birth after birth, Old Age, Disease, and Death.

Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts,

Practical Explanation ( For Example ) :- `1st of all can you tell me every single seconds detail from that time when you born ?? ( i need every seconds detail ?? that what- what you have thought and done on every single second )
can you tell me every single detail of your `1 cheapest Minute Or your whole hour, day, week, month, year or your whole life ??
if you are not able to tell me about this life then what proof do you have that you didn't forget your past ? and that you will not forget this present life in the future ?
that is Fact that Supreme Lord Krishna exists but we posses no such intelligence to understand him.
there is also next life. and i already proved you that no scientist, no politician, no so-called intelligent man in this world is able to understand this Truth. cuz they are imagining. and you cannot imagine what is god, who is god, what is after life etc.
_______
for example :Your father existed before your birth. you cannot say that before your birth your father don,t exists.
So you have to ask from mother, "Who is my father?" And if she says, "This gentleman is your father," then it is all right. It is easy.
Otherwise, if you makes research, "Who is my father?" go on searching for life; you'll never find your father.
( now maybe...maybe you will say that i will search my father from D.N.A, or i will prove it by photo's, or many other thing's which i will get from my mother and prove it that who is my Real father.{ So you have to believe the authority. who is that authority ? she is your mother. you cannot claim of any photo's, D.N.A or many other things without authority ( or ur mother ).
if you will show D.N.A, photo's, and many other proofs from other women then your mother. then what is use of those proofs ??} )
same you have to follow real authority. "Whatever You have spoken, I accept it," Then there is no difficulty. And You are accepted by Devala, Narada, Vyasa, and You are speaking Yourself, and later on, all the acaryas have accepted. Then I'll follow.
I'll have to follow great personalities. The same reason mother says, this gentleman is my father. That's all. Finish business. Where is the necessity of making research? All authorities accept Krsna, the Supreme Personality of Godhead. You accept it; then your searching after God is finished.
Why should you waste your time?
_______
all that is you need is to hear from authority ( same like mother ). and i heard this truth from authority " Srila Prabhupada " he is my spiritual master.
im not talking these all things from my own.
___________
in this world no `1 can be Peace full. this is all along Fact.
cuz we all are suffering in this world 4 Problems which are Disease, Old age, Death, and Birth after Birth.
tell me are you really happy ?? you can,t be happy if you will ignore these 4 main problem. then still you will be Forced by Nature.
___________________
if you really want to be happy then follow these 6 Things which are No illicit s.ex, No g.ambling, No d.rugs ( No tea & coffee ), No meat-eating ( No onion & garlic's )
5th thing is whatever you eat `1st offer it to Supreme Lord Krishna. ( if you know it what is Guru parama-para then offer them food not direct Supreme Lord Krishna )
and 6th " Main Thing " is you have to Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare ".
_______________________________
If your not able to follow these 4 things no illicit s.ex, no g.ambling, no d.rugs, no meat-eating then don,t worry but chanting of this holy name ( Hare Krishna Maha-Mantra ) is very-very and very important.
Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare " and be happy.
if you still don,t believe on me then chant any other name for 5 Min's and chant this holy name for 5 Min's and you will see effect. i promise you it works And chanting at least 16 rounds ( each round of 108 beads ) of the Hare Krishna maha-mantra daily.
____________
Here is no Question of Holy Books quotes, Personal Experiences, Faith or Belief. i accept that Sometimes Faith is also Blind. Here is already Practical explanation which already proved that every`1 else in this world is nothing more then Busy Foolish and totally idiot.
_________________________
Source(s):
every `1 is already Blind in this world and if you will follow another Blind then you both will fall in hole. so try to follow that person who have Spiritual Eyes who can Guide you on Actual Right Path. ( my Authority & Guide is my Spiritual Master " Srila Prabhupada " )
_____________
if you want to see Actual Purpose of human life then see this link : ( triple w ( d . o . t ) asitis ( d . o . t ) c . o . m {Bookmark it })
read it complete. ( i promise only readers of this book that they { he/she } will get every single answer which they want to know about why im in this material world, who im, what will happen after this life, what is best thing which will make Human Life Perfect, and what is perfection of Human Life. ) purpose of human life is not to live like animal cuz every`1 at present time doing 4 thing which are sleeping, eating, s.ex & fear. purpose of human life is to become freed from Birth after birth, Old Age, Disease, and Death.

HomeWork Help Please Respond ASAP!!!

The phrase a number means an arbitrary variable, let's call it x.
Three times a number:
3x
And 18 means we add 18
3x + 18
The word is means equal to, so we set 3x + 18 equal to -39
3x + 18 = -39
This is your algebraic expression. If you want to solve for x, plug it into the [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']search engine[/URL] and you get x = -19

How long will it take $3000 to earn $900 interest at 6% simple interest?

How long will it take $3000 to earn $900 interest at 6% simple interest?
Set up the simple interest equation for the interest piece:
3000 * 0.06t = 900
To solve for t in this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=3000%2A0.06t%3D900&pl=Solve']type it in our search engine [/URL]and we get:
t = [B]5[/B]

How many 4 person committees can be formed from a group of 11 people

How many 4 person committees can be formed from a group of 11 people
We want 11 choose 4, or 11C4.
We type [URL='https://www.mathcelebrity.com/permutation.php?num=11&den=4&pl=Combinations']11C4 into our search engine[/URL] and we get:
[B]330 committees[/B]

How many rides per day to reach 150 rides in 90 days?

How many rides per day to reach 150 rides in 90 days?
Set up a proportion of rides per day where r is the number or rides per day:
150/90 = r/1
Type [URL='https://www.mathcelebrity.com/prop.php?num1=150&num2=r&den1=90&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']this proportion into our search engine[/URL] and we get:
r = 1.66 7

How many ways can 5 people be seated in 5 seats?

How many ways can 5 people be seated in 5 seats?
We have the permutation 5!.
Because the first seat can have 5 different people.
The next seat has 5 - 1 = 4 people since one person is in the first seat
The next seat can have 5 - 2 = 3 people since we have two people in the first two seats
The next seat can have 5 - 3 = 2 people since we have three people in the first three seats
The next seat can have 5 - 4 = 1 people since we have four people in the first four seats
[URL='https://www.mathcelebrity.com/factorial.php?num=5!&pl=Calculate+factorial']Type in 5! into our search engine[/URL], and we get 120.

How many ways can a basketball coach choose to the first five player from a group of 15 players

How many ways can a basketball coach choose to the first five player from a group of 15 players
We use combinations. We want 15 choose 5.
We type this in our search engine and we get:
[URL='https://www.mathcelebrity.com/permutation.php?num=15&den=5&pl=Combinations']15C5[/URL] = [B]3,003 different five player rosters[/B]

How old am I if 400 reduced by 2 times my age is 244?

How old am I if 400 reduced by 2 times my age is 244?
Let my age be a. We're given:
400 - 2a = 244
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D244&pl=Solve']type this equation into our search engine [/URL]and we get:
a = [B]78[/B]

How old am I if 400 reduced by 3 times my age is 124?

How old am I if 400 reduced by 3 times my age is 124?
Let my age be a. We're given an algebraic expression:
[LIST]
[*]3 times my age means we multiply a by 3: 3a
[*]400 reduced by 3 times my age means we subtract 3a from 400:
[*]400 - 3a
[*]The word [I]is[/I] mean an equation, so we set 400 - 3a equal to 124
[/LIST]
400 - 3a = 124
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D124&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]92[/B]

How old am I if: 210 reduced by 3 times my current age is 4 times my current age?

How old am I if: 210 reduced by 3 times my current age is 4 times my current age?
Let your current age be a. We're given:
[LIST]
[*]210 reduced by 3 times current age = 210 - 3a
[*]4 times current age = 4a
[*]The word [I]is[/I] means equal to. So we set 210 - 3a equal to 4a
[/LIST]
210 - 3a = 4a
To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=210-3a%3D4a&pl=Solve']type this equation into our search engine [/URL]and we get:
a = [B]30[/B]

How old am I of 400 reduced by 2 times my age is 224

How old am I of 400 reduced by 2 times my age is 224
[LIST=1]
[*]Let my age be a.
[*]2 times my age: 2a
[*]400 reduced by 2 times my age: 400 - 2a
[*]The phrase [I]is [/I]means an equation. So we set 400 - 2a equal to 224 for our algebraic expression
[/LIST]
[B]400 - 2a = 224
[/B]
If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D224&pl=Solve']type this equation into our search engine[/URL] and we get:
a = [B]88[/B]

Hyperbolic Inverse

Calculates hyperbolic function values:
arcsinh, arccosh, arctanh, arccsch, arcsech, arccoth

I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5

I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5 and add 283. What is my number?
Let the number be n. We're given two expressions:
[LIST=1]
[*]Multiply it by 14 and add 13: 14n + 13
[*]Multiply by 5 and add 283: 5n + 283
[/LIST]
The phrase [I]I get the same answer[/I] means an equation. So we set expression 1 equal to expression 2:
14n + 13 = 5n + 283
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=14n%2B13%3D5n%2B283&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]30[/B]

I am thinking of a number. I multiply it by 14 and add 21. I get the same answer if I multiply by 4

I am thinking of a number. I multiply it by 14 and add 21. I get the same answer if I multiply by 4 and add 141.
Let the number be n.
We have two expressions:
[LIST=1]
[*]Multiply by 14 and add 21 is written as: 14n + 21
[*]Multiply by 4 and add 141 is written as: 4n + 141
[/LIST]
The phrase [I]get the same expression[/I] means they are equal. So we set (1) and (2) equal to each other and solve for n:
14n + 21 = 4n + 141
[URL='https://www.mathcelebrity.com/1unk.php?num=14n%2B21%3D4n%2B141&pl=Solve']Type this equation into our search engine [/URL]to solve for n and we get:
n = [B]12[/B]

I am Thinking of a number. I multiply it by 3 and add 67. I get the same answer If i multiply by 6 s

I am Thinking of a number. I multiply it by 3 and add 67. I get the same answer If i multiply by 6 subtract 8.
Let the number be n. We're given two equal expressions:
[LIST=1]
[*]3n + 67
[*]6n - 8
[/LIST]
Set the expressions equal to each other since they give the [B]same answer[/B]:
3n + 67 = 6n - 8
We have an equation. [URL='https://www.mathcelebrity.com/1unk.php?num=3n%2B67%3D6n-8&pl=Solve']Type this equation into our search engine and we get[/URL]:
n = [B]25[/B]

I am thinking of a number. I multiply it by 7 and add 25. I get the same answer if I multiply by 3 a

I am thinking of a number. I multiply it by 7 and add 25. I get the same answer if I multiply by 3 and add 93. What is my number?
Let the number be n. We're given two expressions:
[LIST]
[*]Multiply the number by 7: 7n
[*]add 25: 7n + 25. <-- Expression 1
[*]Multiply by 3: 3n
[*]Add 93: 3n + 93 <-- Expression 2
[*]The phrase [I]get the same answer[/I] means both expression 1 and expression 2 are equal. So we set them equal to each other:
[/LIST]
7n + 25 = 3n + 93
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=7n%2B25%3D3n%2B93&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]17[/B]

I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13

I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13 and subtract 13.What is my number?
Take a number (n):
The first operation is multiply 5 times n, and then add 39:
5n + 139
The second operation is multiply 13 times n and subtract 13:
13n - 13
Set both operations equal to each other since they result in [I]the same number[/I]
5n + 139 = 13n - 13
[URL='https://www.mathcelebrity.com/1unk.php?num=5n%2B139%3D13n-13&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]n = 19[/B]

I have saved 24 to buy a game which is three-fourth of the total cost of the game how much does the

I have saved 24 to buy a game which is three-fourth of the total cost of the game how much does the game cost ?
Let the cost of the game be c. We're given:
3c/4 = 24
To solve this equation for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=3c&num2=24&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
c = [B]32[/B]

I make 750 toys in 10 hours how many can I make in 4 minutes

I make 750 toys in 10 hours how many can I make in 4 minutes
Convert 10 hours to 4 minutes so we can compare minutes to minutes:
10 hours * 60 hours per minute = 600 minutes
Now set up a proportion of toys to minutes where t is the number of toys made in 4 minutes:
750/600 = t/4
[URL='https://www.mathcelebrity.com/prop.php?num1=750&num2=t&den1=600&den2=4&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine and we get[/URL]:
t = [B]5[/B]

I sold 3 units in 563 attempts. How many did I sell per 100 attempts?

I sold 3 units in 563 attempts. How many did I sell per 100 attempts?
Set up a proportion of sales to attempts where s is the number of sales for 100 attempts:
3/563 = s/100
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=s&den1=563&den2=100&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this in our search engine[/URL], we get:
s = [B]0.532 sales[/B]

I think of a number. I multiply it by 6 and add 3. If my answer is 75, calculate the number I starte

I think of a number. I multiply it by 6 and add 3. If my answer is 75, calculate the number I started with.
Let the number be n.
Multiply it by 6:
6n
Add 3:
6n + 3
If the answer is 75, we set 6n + 3 equal to 75:
6n + 3 = 75
We have an equation. To solve for n, [URL='https://www.mathcelebrity.com/1unk.php?num=6n%2B3%3D75&pl=Solve']we type this equation into our search engine[/URL] and get:
[B]n = 12[/B]

Identify a pair of factors of -35 that has a sum of -2

Identify a pair of factors of -35 that has a sum of -2.
If we [URL='https://www.mathcelebrity.com/factoriz.php?num=-35&pl=Show+Factorization']type in [I]factor -35[/I] into our search engine[/URL], we see 4 factor pairs.
When we add up the factors for each pair, we see [B]7, -5[/B] added together gives us 2.

If (x - 1)/3 = k and k = 2, what is the value of x?

If (x - 1)/3 = k and k = 2, what is the value of x?
If k = 2, we have:
(x - 1)/3 = 2
Cross multiply:
x - 1 = 3 * 2
x - 1 = 6
[URL='https://www.mathcelebrity.com/1unk.php?num=x-1%3D6&pl=Solve']Type this equation into the search engine[/URL], we get:
[B]x = 7[/B]

If 1/2 cup of milk makes 8 donuts. How much cups it takes to make 28 donuts

If 1/2 cup of milk makes 8 donuts. How much cups it takes to make 28 donuts?
Set up a proportion of cups to donuts, where c is the number of cups required to make 28 donuts:
1/2/8 = c/28
Cross multiply:
28(1/2) = 8c
8c = 14
[URL='https://www.mathcelebrity.com/1unk.php?num=8c%3D14&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]c = 1.75[/B]

If 10% of 400 is decreased by 25, the result is

If 10% of 400 is decreased by 25, the result is?
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=10&den1=400&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']10% of 400 using our search engine[/URL] is 40.
The phrase [I]decreased by[/I] means we subtract 25 from 40:
40 - 25 = [B]15[/B]

If 11 times a number is added to twice the number, the result is 104

If 11 times a number is added to twice the number, the result is 104
Let [I]the number[/I] be an arbitrary variable we call x.
11 times a number:
11x
Twice the number (means we multiply x by 2):
2x
The phrase [I]is added to[/I] means we add 2x to 11x:
11x + 2x
Simplify by grouping like terms:
(11 + 2)x = 13x
The phrase [I]the result is[/I] means an equation, so we set 13x equal to 104:
13x = 104 <-- This is our algebraic expression
To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=13x%3D104&pl=Solve']we type it in our search engine[/URL] and we get:
x = [B]8[/B]

If 115% of a number is 460, what is 75% of the number

If 115% of a number is 460, what is 75% of the number.
Let the number be n. We're given:
115% * n = 460
We write 115% of n as 1.15n, so we have:
1.15n = 460
[URL='https://www.mathcelebrity.com/1unk.php?num=1.15n%3D460&pl=Solve']Using our equation calculator[/URL], we get:
n = [B]400
[/B]
The problem asks for 75% of this number, so we [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=75&den1=400&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type in [I]75% of 400[/I] into our search engine[/URL] and get:
[B]300[/B]

If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numer

If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions.
Convert 2 to a fraction with a denominator of 10:
20/2 = 10, so we multiply 2 by 10/10:
2*10/10 = 20/10
Add 2 to the numerator and denominator:
(n + 2)/(d + 2) = 9/10
Cross multiply and simplify:
10(n + 2) = 9(d + 2)
10n + 20 = 9d + 18
Move constants to right side by subtracting 20 from each side and subtracting 9d:
10n - 9d = -2
Subtract 3 from the numerator and denominator:
(n - 3)/(d - 3) = 4/5
Cross multiply and simplify:
5(n - 3) = 4(d - 3)
5n - 15 = 4d - 12
Move constants to right side by adding 15 to each side and subtracting 4d:
5n - 4d = 3
Build our system of equations:
[LIST=1]
[*]10n - 9d = -2
[*]5n - 4d = 3
[/LIST]
Multiply equation (2) by -2:
[LIST=1]
[*]10n - 9d = -2
[*]-10n + 8d = -6
[/LIST]
Now add equation (1) to equation (2)
(10 -10)n (-9 + 8)d = -2 - 6
The n's cancel, so we have:
-d = -8
Multiply through by -1:
d = 8
Now bring back our first equation from before, and plug in d = 8 into it to solve for n:
10n - 9d = -2
10n - 9(8) = -2
10n - 72 = -2
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=10n-72%3D-2&pl=Solve']plug this equation into our search engine[/URL] and we get:
n = 7
So our fraction, n/d = [B]7/8[/B]

If 23.8% of a population is 8,212,000. What is the total population?

If 23.8% of a population is 8,212,000. What is the total population?
This can be written as [I]23.8% of x is 8212000
[/I]
We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=23.8&den1=8212000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type this expression into our search engine[/URL] and we get:
[B]1,954,456[/B]

if 3/15 is equivalent to 45/a, find a

if 3/15 is equivalent to 45/a, find a.
Set up the proportion:
3/15 = 45/a
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=45&den1=15&den2=a&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
a = [B]225[/B]

if 30% of 40% of x is 18.6, find the value of x

if 30% of 40% of x is 18.6, find the value of x
30% is 0.3
40% is 0.4
So we have:
0.3 * 0.4 * x = 18.6
Simplifying, we get:
0.12x = 18.6
[URL='https://www.mathcelebrity.com/1unk.php?num=0.12x%3D18.6&pl=Solve']Typing this equation into our search engine[/URL], we get:
x = [B]155[/B]

If 3r = 18, what is the value of 6r + 3?

If 3r = 18, what is the value of 6r + 3?
A) 6
B) 27
C) 36
D) 39
If [URL='https://www.mathcelebrity.com/1unk.php?num=3r%3D18&pl=Solve']we type in the equation 3r = 18 into our search engine[/URL], we get:
r = 6
Take r = 6, and subtitute it into 6r + 3:
6(6) + 3
36 + 3
[B]39, or answer D[/B]

If 4 times a number is added to 9, the result is 49

If 4 times a number is added to 9, the result is 49.
[I]A number[/I] means an arbitrary variable, let's call it x.
4 [I]times a number[/I] means we multiply x by 4
4x
[I]Added to[/I] 9 means we add 9 to 4x
4x + 9
[I]The result is[/I] means we have an equation, so we set 4x + 9 equal to 49
[B]4x + 9 = 49[/B] <-- This is our algebraic expression
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%2B9%3D49&pl=Solve']we type it in the search engine[/URL] and get x = 10

If 4(x-9)=3x-8x, what is x?

[SIZE=5]If 4(x-9)=3x-8x, what is x?
[/SIZE]
[SIZE=4]Multiply through:
4x - 36 = 3x - 8x
Group like terms:
4x - 36 = -5x
[/SIZE]
[URL='https://www.mathcelebrity.com/1unk.php?num=4x-36%3D-5x&pl=Solve'][SIZE=4]Typing this equation into the search[/SIZE][/URL][SIZE=4][URL='https://www.mathcelebrity.com/1unk.php?num=4x-36%3D-5x&pl=Solve'] engine[/URL], we get:
[B]x = 4[/B][/SIZE]

If 50 out of 250 people die. How many people died per 10 people

If 50 out of 250 people die. How many people died per 10 people
We set up a proportion of deaths to total people where d is the number of deaths for 10 people. We have:
50/250 = d/10
To solve this proportion for d, we [URL='https://www.mathcelebrity.com/prop.php?num1=50&num2=d&den1=250&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
d = [B]2[/B]

if 65/100 = 117/x, what is x

if 65/100 = 117/x, what is x
Type the [URL='https://www.mathcelebrity.com/prop.php?num1=65&num2=117&den1=100&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion [I]65/100 = 117/x [/I]into our search engine[/URL] and we get:
x = [B]180[/B]

If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integ

If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integer.
[LIST]
[*]Let the integer be "x".
[*]Square the integer: x^2
[*]7 times the square: 7x^2
[*]5 times the integer: 5x
[*]Add them together: 7x^2 + 5x
[*][I]The result is[/I] means an equation, so we set 7x^2 + 5x equal to 2
[/LIST]
7x^2 + 5x = 2
[U]This is a quadratic equation. To get it into standard form, we subtract 2 from each side:[/U]
7x^2 + 5x - 2 = 2 - 2
7x^2 + 5x - 2 = 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=7x%5E2%2B5x-2%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get two solutions:
[LIST=1]
[*]x = 2/7
[*]x= -1
[/LIST]
The problem asks for an integer, so our answer is x[B] = -1[/B].
[U]Let's check our work by plugging x = -1 into the quadratic:[/U]
7x^2 + 5x - 2 = 0
7(-1)^2 + 5(-1) - 2 ? 0
7(1) - 5 - 2 ? 0
0 = 0
So we verified our answer, [B]x = -1[/B].

If 72 is added to a number it will be 4 times as large as it was originally

If 72 is added to a number it will be 4 times as large as it was originally
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
72 added to a number:
x + 72
4 times as large as it was originally means we take the original number x and multiply it by 4:
4x
Now, the phrase [I]it will be[/I] means an equation, so we set x + 72 equal to 4x to get our final algebraic expression:
[B]x + 72 = 4x[/B]
[B][/B]
If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B72%3D4x&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]24[/B]

If 800 feet of fencing is available, find the maximum area that can be enclosed.

If 800 feet of fencing is available, find the maximum area that can be enclosed.
Perimeter of a rectangle is:
2l + 2w = P
However, we're given one side (length) is bordered by the river and the fence length is 800, so we have:
So we have l + 2w = 800
Rearranging in terms of l, we have:
l = 800 - 2w
The Area of a rectangle is:
A = lw
Plug in the value for l in the perimeter into this:
A = (800 - 2w)w
A = 800w - 2w^2
Take the [URL='https://www.mathcelebrity.com/dfii.php?term1=800w+-+2w%5E2&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']first derivative[/URL]:
A' = 800 - 4w
Now set this equal to 0 for maximum points:
4w = 800
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%3D800&pl=Solve']Typing this equation into the search engine[/URL], we get:
w = 200
Now plug this into our perimeter equation:
l = 800 - 2(200)
l = 800 - 400
l = 400
The maximum area to be enclosed is;
A = lw
A = 400(200)
A = [B]80,000 square feet[/B]

If 9 is added to 1/3 of a number, the result is 15. What is the number?

If 9 is added to 1/3 of a number, the result is 15. What is the number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
1/3 of a number means we multiply x by 1/3:
x/3
9 is added to 1/3 of a number:
x/3 + 9
The phrase [I]the result is[/I] means an equation. so we set x/3 + 9 equal to 15
x/3 + 9 = 15
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2F3%2B9%3D15&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]18[/B]

If a machine produces 100 bags per minute how long will it take to make 40,000

If a machine produces 100 bags per minute how long will it take to make 40,000
100 bags/ per minute = 40,000 bags / m
Cross multiply
100m = 40000
[URL='https://www.mathcelebrity.com/1unk.php?num=100m%3D40000&pl=Solve']Type this equation into the search engine[/URL] and we get:
m = [B]400[/B]

if a number is added to its square, it equals 20

if a number is added to its square, it equals 20.
Let the number be an arbitrary variable, let's call it n.
The square of the number means we raise n to the power of 2:
n^2
We add n^2 to n:
n^2 + n
It equals 20 so we set n^2 + n equal to 20
n^2 + n = 20
This is a quadratic equation. So [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn%3D20&pl=Solve+Quadratic+Equation&hintnum=+0']we type this equation into our search engine[/URL] to solve for n and we get two solutions:
[B]n = (-5, 4)[/B]

if a number is added to its square, the result is 72. find the number

if a number is added to its square, the result is 72. find the number.
Let the number be n. We're given:
n + n^2 = 72
Subtract 72 from each side, we get:
n^2 + n - 72 = 0
This is a quadratic equation. [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-72%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']We type this equation into our search engine[/URL], and we get:
[B]n = 8 and n = -9[/B]

if a number is tripled the result is 60

if a number is tripled the result is 60
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Triple the number means we multiply by 3:
3x
The phrase [I]the result is[/I] means an equation, so we set 3x equal to 60:
[B]3x = 60 <-- This is our algebraic expression
[/B]
If you want to solve this equation, then [URL='https://www.mathcelebrity.com/1unk.php?num=3x%3D60&pl=Solve']you type in 3x = 60 into the search engine[/URL] and get:
x = 20

if ballons are on sale at 15 for$3, whats the cost for a ballon? a)50cents b)25cost c)20cents d)20 d

if ballons are on sale at 15 for$3, whats the cost for a ballon? a)50cents b)25cost c)20cents d)20 dollars
Let c be the cost of 1 balloon. We set up a proportion of balloons to cost:
15/3 = 1/c
To solve this proportion for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=1&den1=3&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
c = [B]0.2 or 20 cents[/B]

If EF = 7x , FG = 3x , and EG = 10 , what is EF?

If EF = 7x , FG = 3x , and EG = 10 , what is EF?
By segment addition:
EF + FG = EG
7x + 3x = 10
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=7x%2B3x%3D10&pl=Solve']type it in our search engine[/URL] and we get:
x = 1
Evaluating EF = 7x with x = 1, we get:
EF = 7 * 1
EF = [B]7[/B]

If Emma reads 1 page of a book in 44 seconds, how many pages will she read in 15 minutes

If Emma reads 1 page of a book in 44 seconds, how many pages will she read in 15 minutes
Convert 15 minutes to seconds:
15 minutes = 60 * 15 = 900 seconds
Set up a proportion of pages read to seconds where p is the number of pages read in 900 seconds (15 minutes):
1/44 = p/900
[URL='https://www.mathcelebrity.com/prop.php?num1=1&num2=p&den1=44&den2=900&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
p = [B]20.45[/B]

If Frank’s age is double of Willis’ age and the sum of their ages is 42. What are their ages?

If Frank’s age is double of Willis’ age and the sum of their ages is 42. What are their ages?
Let Frank's age be f. Let Willis's age be w. We're given two equations:
[LIST=1]
[*]f = 2w <-- Double means multiply by 2
[*]f + w = 42
[/LIST]
Substitute equation (1) into equation (2):
2w + w = 42
To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=2w%2Bw%3D42&pl=Solve']type this equation into our search engine[/URL]. We get:
w = [B]14
[/B]
Now, take w = 14, and substitute it back into equation (1) to solve for f:
f = 2(14)
f = [B]28[/B]

If half the number is added to twice the number, the answer is 50

If half the number is added to twice the number, the answer is 50.
Let the number be n. Half is also written as 0.5, and twice is written by multiplying by 2. We have:
0.5n + 2n = 50
[URL='https://www.mathcelebrity.com/1unk.php?num=0.5n%2B2n%3D50&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]n = 20[/B]

If I add 8 to the number and then multiply the result by 6 I get the same answer as when I add 58 to

If I add 8 to the number and then multiply the result by 6 I get the same answer as when I add 58 to a number. Form an equation
Let the number be n. We're given:
6(n + 8) = n + 58
Multiply through:
6n + 48 = n + 58
To solve this equation for n, [URL='https://www.mathcelebrity.com/1unk.php?num=6n%2B48%3Dn%2B58&pl=Solve']we type it into our search engine[/URL] and we get:
n = [B]2[/B]

If I have a reading average of 2 hours 30 minutes 0 seconds per 93.25 pages, how long would it take

If I have a reading average of 2 hours 30 minutes 0 seconds per 93.25 pages, how long would it take me to read 58 pgs?
Set up a proportion, of reading time to pages where m is the number of minutes it takes you to read 58 pages.
2 hours and 30 minutes is:
60(2) + 30
120 + 30
150 minutes
Our proportion is:
150/93.25 = m/58
[URL='https://www.mathcelebrity.com/prop.php?num1=150&num2=m&den1=93.25&den2=58&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get:
[B]m = 93.3 minutes, or about 1 hour, 33 minutes[/B]

If I make 40,000 dollars every 15 minutes then how long will it take me to make a million

If I make 40,000 dollars every 15 minutes then how long will it take me to make a million
Let f be the number of fifteen minute blocks. We're given:
40000f = 1000000
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=40000f%3D1000000&pl=Solve']type this equation into our search engine[/URL] and we get:
f = 25
Total minutes = Fifteen minute blocks (f) * 15 minutes
Total minutes = 25 * 15
Total minutes = [B]375 minutes or 6 hours and 15 minutes[/B]

If i triple the number then subtract 7 the answer is 2. What is the number

If i triple the number then subtract 7 the answer is 2. What is the number
Let the number be x.
Triple the number:
3x
Subtract 7
3x - 7
The answer is 2 means we set:
[B]3x - 7 = 2[/B]
This is our algebraic expression. To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D2&pl=Solve']we type this problem into the search engine[/URL] and get [B]x = 3[/B].

If power is big, you can assume:

If power is big, you can assume:
a. The difference between the means is more likely to be detected
b. The significance level set by the researcher must be high
c. We increase the probability of type I error
d. Your study result will be more likely to be inconclusive
[B]b. The significance level set by the researcher must be high[/B]

If QR = 16, RS = 4x ? 17, and QS = x + 20, what is RS?

If QR = 16, RS = 4x ? 17, and QS = x + 20, what is RS?
From the segment addition rule, we have:
QR + RS = QS
Plugging our values in for each of these segments, we get:
16 + 4x - 17 = x + 20
To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2B4x-17%3Dx%2B20&pl=Solve']we type it in our search engine[/URL] and we get:
x = 7
Take x = 7 and substitute it into RS:
RS = 4x - 17
RS = 4(7) - 17
RS = 28 - 17
RS = [B]11[/B]

If Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how ma

If Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how many of each coin does he have?
Using q for quarters and n for nickels, and using 525 cents as $5.25, we're given two equations:
[LIST=1]
[*]q = 4n
[*]0.25q + 0.05n = 5.25
[/LIST]
Substitute equation (1) into equation (2) for q:
0.25(4n) + 0.05n = 5.25
Multiply through and simplify:
n + 0.05n = 5.25
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B0.05n%3D5.25&pl=Solve']type it in our search engine[/URL] and we get:
n = [B]5
[/B]
To get q, we plug in n = 5 into equation (1) above:
q = 4(5)
q = [B]20[/B]

If the equation of a line passes through the points (1, 3) and (0, 0), which form would be used to w

If the equation of a line passes through the points (1, 3) and (0, 0), which form would be used to write the equation of the line?
[URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=3&slope=+&xtwo=0&ytwo=0&bvalue=+&pl=You+entered+2+points']Typing (1,3),(0,0) into the search engine[/URL], we get a point-slope form:
[B]y - 3 = 3(x - 1)[/B]
If we want mx + b form, we have:
y - 3 = 3x - 3
Add 3 to each side:
[B]y = 3x[/B]

If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide

If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide must the field be?
The perimeter of a rectangle P, is denoted as:
P = 2l + 2w
We're given l = 25, and P = 120, so we have
2(25) + 2w = 120
Simplify:
2w + 50 = 120
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B50%3D120&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 35[/B]

If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, th

If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, then what are the length and width?
The perimeter (P) of a rectangle is:
2l + 2w = P
We're given P = 44, so we substitute this into the rectangle perimeter equation:
2l + 2w = 44
We're also given w = 0.5l - 2. Substitute the into the Perimeter equation:
2l + 2(0.5l - 2) = 44
Multiply through and simplify:
2l + l - 4 = 44
Combine like terms:
3l - 4 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=3l-4%3D44&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]l = 16[/B]
Substitute this back into the equation w = 0.5l - 2
w = 0.5(16) - 2
w = 8 - 2
[B]w = 6[/B]

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find th

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find the time taken by aeroplane to cover 1200m initially.
We know from the distance formula (d) using rate (r) and time (t) that:
d = rt
Regular speed:
1200 = rt
Divide each side by t, we get:
r = 1200/t
Reduced speed. 20 minutes = 60/20 = 1/3 of an hour. So we multiply 1,200 by 3
3600 = (r - 40)(t + 1/3)
If we multiply 3 by (t + 1/3), we get:
3t + 1
So we have:
3600 = (r - 40)(3t + 1)
Substitute r = 1200/t into the reduced speed equation:
3600 = (1200/t - 40)(3t + 1)
Multiply through and we get:
3600 = 3600 - 120t + 1200/t - 40
Subtract 3,600 from each side
3600 - 3600 = 3600 - 3600 - 120t + 1200/t - 40
The 3600's cancel, so we get:
- 120t + 1200/t - 40 = 0
Multiply each side by t:
-120t^2 - 40t + 1200 = 0
We've got a quadratic equation. To solve for t, [URL='https://www.mathcelebrity.com/quadratic.php?num=-120t%5E2-40t%2B1200%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this in our search engine[/URL] and we get:
t = -10/3 or t = 3. Since time [I]cannot[/I] be negative, our final answer is:
[B]t = 3[/B]

If there are 8 girls entered in a race, how many different ways can the runners place first, second,

If there are 8 girls entered in a race, how many different ways can the runners place first, second, and third?
We want 8 choose 3, or 8C3.
[URL='https://www.mathcelebrity.com/permutation.php?num=8&den=3&pl=Combinations']Type 8C3 into the search engine[/URL], and we get [B]56[/B] different ways to place first, second, and third.

If thrice a number is increased by 11,the result is 35. What is the number

If thrice a number is increased by 11,the result is 35. What is the number?
[LIST]
[*]The phrase [I]a number [/I]means an arbitrary variable. Let's call it x.
[*]Thrice means multiply by 3, so we have 3x
[*]Increased by 11 means we add 11, so we have 3x + 11
[*]The [I]result is[/I] means an equation, so we set 3x + 11 equal to 35
[/LIST]
3x + 11 = 35 <-- This is our algebraic expression
The problem ask us to solve the algebraic expression.
[URL='https://www.mathcelebrity.com/1unk.php?num=3x%2B11%3D35&pl=Solve']Typing this problem into our search engine[/URL], we get [B]x = 8[/B].

if two angles are supplementary and congruent then they are right angles

if two angles are supplementary and congruent then they are right angles
Let the first angle be x. Let the second angle be y.
Supplementary angles means their sum is 180:
x + y = 180
We're given both angles are congruent, meaning equal. So we set x = y:
y + y = 180
To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=y%2By%3D180&pl=Solve']type this equation into our search engine[/URL] and we get:
y = [B]90. <-- 90 degrees is a right angle, so this is TRUE[/B]

If x is 18 when y is 6, find y when x is 21

If x is 18 when y is 6, find y when x is 21
Set up a proportion of x to y:
18/6 = 21/y
To solve this proportion for y, we[URL='https://www.mathcelebrity.com/prop.php?num1=18&num2=21&den1=6&den2=y&propsign=%3D&pl=Calculate+missing+proportion+value'] type it in our search engine[/URL] and we get:
y = [B]7[/B]

If x/2y = 3/4, what is the value of y/x?

If x/2y = 3/4, what is the value of y/x?
Cross multiply this proportion:
4x = 3(2y)
4x = 6y
Divide each side by x:
4x/x = 6y/x
The x's cancel, and we have:
6y/x = 4
Divide each side by 6:
6y/6x = 4/6
The 6's on the left cancel, we have:
y/x = 4/6
We can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F6&frac2=3%2F8&pl=Simplify']Type in Simplify 4/6 into the search engine[/URL], and we get 2/3.
y/x = [B]2/3[/B]

If y=2x and y=18, what is the value of x

If y=2x and y=18, what is the value of x
Since y = 2x [B]and[/B] y = 18, we set 2x equals to 18 since they both equal y
2x = 18
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D18&pl=Solve']Type this equation into our search engine[/URL] and we get:
x = [B]9[/B]

if you add 35 to twice a number, the result is 17. What is the number?

if you add 35 to twice a number, the result is 17. What is the number?
A number is represented by a variable, let's call it "x".
Twice a number means we multiply by 2 --> 2x
Add 35
2x + 35
Now set that entire expression equal to 17
2x + 35 = 17
[URL='http://www.mathcelebrity.com/1unk.php?num=2x%2B35%3D17&pl=Solve']Plug that into the search engine to solve for x[/URL]
[B]x = -9[/B]

if you add 7 to 2x, the result is 17

if you add 7 to 2x, the result is 17
Add 7 to 2x:
2x + 7
The phrase [I]the result is[/I] means an equation, so we set 2x + 7 = 17
[B]2x + 7 = 17 [/B] <-- This is our algebraic expression
Now, if you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B7%3D17&pl=Solve']type in 2x + 7 = 17 into the search engine[/URL], and we get [B]x = 5[/B].

If you can buy 1?3 of a box of chocolates for 6 dollars, how much can you purchase for 4 dollars? Wr

If you can buy 1?3 of a box of chocolates for 6 dollars, how much can you purchase for 4 dollars? Write your answer as a fraction of a box.
Set up a proportion of dollars to boxes where b is the number of boxes for $4:
6/1/3 = 4/b
Cross multiply:
6b = 4/3
Multiply each side by 1/6 to isolate b:
b = 4/18
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=4&num2=18&num3=&pl=GCF+and+LCM']Type in GCF(4,18) into the search engine[/URL]. We get a greatest common factor of 2.
Divide 4 and 18 in the fraction by 2. We get the reduced fraction of:
[B]b = 2/9[/B]

If you have $272, and you spend $17 each day, how long would it be until you had no money left?

If you have $272, and you spend $17 each day, how long would it be until you had no money left?
Let d be the number of days. We have a balance expression of:
272 - 17d
We want to know when the balance is 0, so we set 272 - 17d equal to 0.
272 - 17d = 0
To solve for d, we [URL='http://272 - 17d = 0']type this equation into our search engine[/URL] and we get:
d = [B]16[/B]

If you take a Uber and they charge $5 just to show up and $1.57 per mile, how much will it cost you

If you take a Uber and they charge $5 just to show up and $1.57 per mile, how much will it cost you to go 12 miles? (Assume no tip.)
a. Create an equation from the information above.
b. Identify the slope in the equation?
c. Calculate the total cost of the ride?
2. With the same charges as #1, how many miles could you go with $50, if you also gave a $7.50 tip? (Challenge Question! Hint, you only have a $50, exactly, with you
a. Cost Equation C(m) for m miles is as follows:
[B]C(m) = 1.57m + 5
[/B]
b.
Slope of the equation is the coefficient for m, which is [B]1.57
[/B]
c.
Total cost of the ride for m = 12 miles is:
C(12) = 1.57(12) + 5
C(12) = 18.84 + 5
C(12) = [B]23.84
[/B]
d.
If you give a 7.50 tip, we subtract the tip from the $50 to start with a reduced amount:
50 - 7.50 = 42.50
So C(m) = 42.50
1.57m + 5 = 42.50
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.57m%2B5%3D42.50&pl=Solve']type it in our search engine[/URL] and we get:
m = 23.89
Since we deal in full miles, we round our answer down to m = [B]23[/B]

If you toss a fair coin 6 times, what is the probability of getting all tails?

If you toss a fair coin 6 times, what is the probability of getting all tails?
We [URL='https://www.mathcelebrity.com/cointoss.php?hts=TTTTTT&hct=+2&tct=+1&fct=+5>=no+more+than&nmnl=+2&htpick=tails&calc=1&montect=500&pl=Calculate+Probability']type in our search engine [I]TTTTTT [/I]and we get[/URL]:
P(TTTTTT) = [B]1/64 or 0.015625[/B]

If your parents give you $20 per week and $1.50 per chore, how many chores would you have to do to e

If your parents give you $20 per week and $1.50 per chore, how many chores would you have to do to earn a total of $33.50 that week?
Let c be the number of chores. We're given the equation:
1.50c + 20 = 33.50
To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.50c%2B20%3D33.50&pl=Solve']type it in our search engine [/URL]and we get:
c = [B]9[/B]

Imagine a researcher posed a null hypothesis that in a certain community, the average energy expendi

Imagine a researcher posed a null hypothesis that in a certain community, the average energy expenditure should be 2,100 calories per day. He randomly sampled 100 people in that community. After he computed the t value by calculating a two-tailed t-statistic, he found that the probability value was 0.10. Thus, he concluded:
a. The average energy expenditure was bigger than 2,100 calories per day
b. The average energy expenditure was smaller than 2,100 calories per day
c. He could not reject the null hypothesis that the average energy expenditure was 2,100 calories per day
d. The average energy expenditure was either more than 2,100 calories per day or less than 2,100 calories per day
[B]c. He could not reject the null hypothesis that the average energy expenditure was 2,100 calories per day[/B]
[I]p-value is higher than 0.05[/I]

Imagine a researcher wanted to test the effect of the new drug on reducing blood pressure. In this s

Imagine a researcher wanted to test the effect of the new drug on reducing blood pressure. In this study, there were 50 participants. The researcher measured the participants' blood pressure before and after the drug intake. If we want to compare the mean blood pressure from the two time periods with a two-tailed t test, how many degrees of freedom are there?
a. 49
b. 50
c. 99
d. 100
[B]a. 49[/B]
Degrees of Freedom = n - 1
Degrees of Freedom = 50 - 1
Degrees of Freedom = 49

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He r

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. What's the sample [U][B]standard deviation[/B][/U]?
[B]20.79182532[/B] using stdev.s in excel or also found on our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics#standard_deviation']statistics calculator[/URL]

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He r

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. What's the [B][U]standard error of the mean[/U][/B]?
9.29839 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics#standard_error_of_the_mean']statistics calculator[/URL]

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He r

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. The researcher posed a null hypothesis that the average weight for boys in that high school should be 100 lbs. What is the [B][U]absolute value[/U][/B] of calculated t that we use for testing the null hypothesis?
Mean is 109.4 and Standard Deviation = 20.79182532 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']statistics calculator[/URL]
Now use those values and calculate the t-value
Abs(t value) = (100 - 109.4)/ 20.79182532/sqrt(5)
Abs(tvalue) = [B]1.010928029[/B]

In 16 years, Ben will be 3 times as old as he is right now

In 16 years, Ben will be 3 times as old as he is right now.
Let Ben's age today be a. We're given:
a + 16 = 3a
[URL='https://www.mathcelebrity.com/1unk.php?num=a%2B16%3D3a&pl=Solve']Type this equation into the search engine[/URL], and we get:
a = [B]8[/B]

In 1996 Ato Boldon of UCLA ran the 100-meter dash in 9.92 seconds. In 1969 John Carlos of San Jose S

In 1996 Ato Boldon of UCLA ran the 100-meter dash in 9.92 seconds. In 1969 John Carlos of San Jose State ran the 100-yard dash in 9.1 seconds. Which runner had the faster average speed?
We [URL='https://www.mathcelebrity.com/linearcon.php?quant=100&type=yard&pl=Calculate']convert yards to meters using our conversion calculator[/URL] and we get:
100 yards = 91.44 meters
Now we set up a proportion of time per meter:
[LIST]
[*]Ato Boldon: 9.92/100 = 0.992 per meter
[*]John Carlos: 9.1/91.44 = 0.995 per meter
[/LIST]
[B]Since Ato Boldon's time was [I]less per meter[/I], he had the faster average speed[/B]

In 20 years charles will be 3 times as old as he is now. How old is he now?

In 20 years charles will be 3 times as old as he is now. How old is he now?
Let Charles's age be a today. We're given:
a + 20 = 3a
[URL='https://www.mathcelebrity.com/1unk.php?num=a%2B20%3D3a&pl=Solve']If we type this equation into our search engine[/URL], we get:
[B]a = 10
[/B]
Let's check our work in our given equation:
10 + 20 ? 3(10)
30 = 30 <-- Checks out!

In 56 years, Stella will be 5 times as old as she is right now.

In 56 years, Stella will be 5 times as old as she is right now.
Let Stella's age be s. We're given:
s + 56 = 5s
[URL='https://www.mathcelebrity.com/1unk.php?num=s%2B56%3D5s&pl=Solve']Type this equation into our search engine[/URL], and we get:
[B]s = 14[/B]

In a basketball game, you make 8 of 20 free throws. If you continue this for the next 50 free throws

In a basketball game, you make 8 of 20 free throws. If you continue this for the next 50 free throws, how many can you expect to make?
We set up a [U][I]proportion[/I][/U] of made free throws to attempts.
8/20 = m/50 where m is the number of made free throws in 50 attempts.
[URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=m&den1=20&den2=50&propsign=%3D&pl=Calculate+missing+proportion+value']We type 8/20 = m/50 into the search engine[/URL] and get [B]m = 20[/B].

In a certain Algebra 2 class of 26 students, 18 of them play basketball and 7 of them play baseball.

In a certain Algebra 2 class of 26 students, 18 of them play basketball and 7 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Students play either basketball only, baseball only, both sports, or no sports. Let the students who play both sports be b. We have:
b + 18 + 7 - 5 = 26 <-- [I]We subtract 5 because we don't want to double count the students who played a sport who were counted already
[/I]
We [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B18%2B7-5%3D26&pl=Solve']type this equation into our search engine[/URL] and get:
b = [B]6[/B]

in a city, the record monthly high temperature for March is 56°F. The record monthly low for March i

in a city, the record monthly high temperature for March is 56°F. The record monthly low for March is -4°F. What is the range of temperatures for the month of March
Range = High - Low
Range = 56 - -4
Range = 56 + 4 [I]since double negative is positive[/I]
Range = [B]60[/B]

In a newspaper, it was reported that yearly robberies in Springfield were up 50% to 351 in 2013 from

In a newspaper, it was reported that yearly robberies in Springfield were up 50% to 351 in 2013 from 2012. How many robberies were there in Springfield in 2012?
Let the robberies in 2012 be r. We're given the following equation:
1.5r = 351 <-- We write a 50% increase as 1.5
To solve this equation for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.5r%3D351&pl=Solve']type it into our search engine[/URL] and we get:
r = [B]234[/B]

In a theatre audience of 500 people, 80 percent were adults. How many children were in the audience

In a theatre audience of 500 people, 80 percent were adults. How many children were in the audience?
If 80% were adults, this means 100% - 80% = 20% were children.
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=20&den1=500&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']We type the expression 20% of 500 into our search engine[/URL] and get [B]100 children[/B]

In an algebra test, the highest grade was 50 points higher than the lowest grade. The sum of the two

In an algebra test, the highest grade was 50 points higher than the lowest grade. The sum of the two grades was 180.
Let the high grade be h and the low grade be l. We're given:
[LIST=1]
[*]h = l + 50
[*]h + l = 180
[/LIST]
Substitute equation (1) into equation (2) for h
l + 50 + l = 180
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=l%2B50%2Bl%3D180&pl=Solve']we type it in our search engine[/URL] and we get:
l = [B]65
[/B]
Now, we take l = 65 and substitute it into equation (1) to solve for h:
h = 65 + 50
h = [B]115[/B]

In Maricopa County, 5 persons are to be elected to the Board of Supervisors. If 8 persons are candid

In Maricopa County, 5 persons are to be elected to the Board of Supervisors. If 8 persons are candidates, how many different arrangements are possible?
We want 8 choose 5, or 8C5. [URL='http://www.mathcelebrity.com/permutation.php?num=8&den=5&pl=Combinations']Typing this into the search engine[/URL] we get [B]56[/B].

In one day, a store sells 14 pairs of jeans. The 14 jeans represent 20% of the total number of items

In one day, a store sells 14 pairs of jeans. The 14 jeans represent 20% of the total number of items sold that day. How many items did the store sell in one day? Explain or show how you got your answer.
14 = 20%s where s is the number of items sold in one day.
We can write 20% as 0.2, so we have:
0.2s = 14
[URL='https://www.mathcelebrity.com/1unk.php?num=0.2s%3D14&pl=Solve']Type this equation into the search engine[/URL], and we get:
s = [B]70[/B]

In the last year a library bought 237 new books and removed 67 books. There were 5745 books in the l

In the last year a library bought 237 new books and removed 67 books. There were 5745 books in the library at the end of the year. How many books were in the library at the start of the year
Let the starting book count be b. We have:
[LIST]
[*]We start with b books
[*]Buying 237 books means we add (+237)
[*]Removing 67 books means we subtract (-67)
[*]We end up with 5745 books
[/LIST]
Our change during the year is found by the equation:
b + 237 - 67 = 5745
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B237-67%3D5745&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]5575[/B]

In the past year, Yoko watched 76 movies that she thought were very good. She watched 80 movies ove

In the past year, Yoko watched 76 movies that she thought were very good. She watched 80 movies over the whole year. Of the movies she watched, what percentage did she think were very good?
[URL='http://www.mathcelebrity.com/perc.php?num=76&den=80&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Enter 76/80 into our search engine to get 95%[/URL].

In Trina's desk drawer, there are 15 paper clips and 18 rubber bands. In Kirk's office supply tray,

In Trina's desk drawer, there are 15 paper clips and 18 rubber bands. In Kirk's office supply tray, there are 13 paper clips and 16 rubber bands. Who has a higher ratio of paper clips to rubber bands?
Trina: 15/18
Kirk: 13/16
We want common denominators to compare, so we get a greatest common factor (GCF) for 16 and 18.
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=16&num2=18&num3=&pl=GCF+and+LCM']Running this through our search engine[/URL], we get GCF(16, 18) = 144
For Trina, 144/18 = 8
For Kirk, 144/16 = 9
We multiply Trina's fraction, top and bottom by 8:
15 * 8 / 18 * 8
120/144
We multiply Trina's fraction, top and bottom by 8:
13 * 8 / 16 * 8
104/144
[B]Trina[/B] has more in her numerator, so her ratio of paper clips to rubber bands is greater.

In which quadrant is the point (2,negative 6) located?

In which quadrant is the point (2,negative 6) located?
We have the point (2, -6). It lies in Quadrant IV.
to get this, [URL='https://www.mathcelebrity.com/polrectcord.php?num=2%2C-6&pl=Show+Detail#Quadrant']type in (2, -6) to the search engine[/URL], and click "Quadrant".

Is 30 a solution to 2x + 5 = 3x - 25

Is 30 a solution to 2x + 5 = 3x - 25
Let's test x = 30 into our equation:
2(30) + 5 ? 3(30) - 25
60 + 5 ? 90 - 25
65 = 65
[B]Yes, x = 30 is a solution[/B].
If you wanted to solve for x with simplification, you can [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B5%3D3x-25&pl=Solve']type it in our search engine[/URL] and get:
x = 30

Isabel is making face mask. She spends $50 on supplies and plans on selling them for $4 per mask. Ho

Isabel is making face mask. She spends $50 on supplies and plans on selling them for $4 per mask. How many mask does have to make in order to make a profit equal to $90?
[U]Set up the cost function C(m) where m is the number of masks:[/U]
C(m) = supply cost
C(m) = 50
[U]Set up the cost function R(m) where m is the number of masks:[/U]
R(m) = Sale Price * m
R(m) = 4m
[U]Set up the profit function P(m) where m is the number of masks:[/U]
P(m) = R(m) - C(m)
P(m) = 4m - 50
The problems asks for profit of 90, so we set P(m) = 90:
4m - 50 = 90
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=4m-50%3D90&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]35[/B]

Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only

[SIZE=4]Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only 5 times as old as William?
[U]Express Ishaan and William's age since today where y is the number of years since today, we have:[/U]
i = 72+y
w = 4+y
[U]We want the time for Ishaan age will be 5 times William's age:[/U]
i = 5w
72 + y = 5(4 + y)
We [URL='https://www.mathcelebrity.com/1unk.php?num=72%2By%3D5%284%2By%29&pl=Solve']plug this equation into our search engine [/URL]and get:
y = [B]13[/B]
[/SIZE]

It costs $2.50 to rent bowling shoes. Each game costs $2.25. You have $9.25. How many games can you

It costs $2.50 to rent bowling shoes. Each game costs $2.25. You have $9.25. How many games can you bowl. Writing an equation and give your answer.
Let the number of games be g. we have the function C(g):
C(g) = cost per game * g + bowling shoe rental
C(g) = 2.25g + 2.50
The problem asks for g when C(g) = 9.25
2.25g + 2.50 = 9.25
To solve this equation, we[URL='https://www.mathcelebrity.com/1unk.php?num=2.25g%2B2.50%3D9.25&pl=Solve'] type it in our search engine[/URL] and we get:
g = [B]3[/B]

it costs $75.00 for a service call from shearin heating and air conditioning company. the charge for

it costs $75.00 for a service call from shearin heating and air conditioning company. the charge for labor is $60.00 . how many full hours can they work on my air conditioning unit and still stay within my budget of $300.00 for repairs and service?
Our Cost Function is C(h), where h is the number of labor hours. We have:
C(h) = Variable Cost * Hours + Fixed Cost
C(h) = 60h + 75
Set C(h) = $300
60h + 75 = 300
[URL='https://www.mathcelebrity.com/1unk.php?num=60h%2B75%3D300&pl=Solve']Running this problem in the search engine[/URL], we get [B]h = 3.75[/B].

It takes 3/4 of an hour to complete a puzzle. How many puzzles can Cindy finish in 3 hours?

It takes 3/4 of an hour to complete a puzzle. How many puzzles can Cindy finish in 3 hours?
We setup a proportion of time to puzzles where p is the number of puzzles Cindy can complete in 3 hours:
3/4/1 = 3/p
Dividing by 1 means the same as the original fraction, so we have:
3/4 = 3/p
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=3&den1=4&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into the search engine[/URL], we get:
p = [B]4[/B]

It takes 60 minutes for 7 people to paint 5 walls. How many minutes does it take 10 people to paint

It takes 60 minutes for 7 people to paint 5 walls. How many minutes does it take 10 people to paint 10 walls?
Rate * Time = Output
Let "Rate" (r) be the rate at which [B]one person[/B] works.
So we have:
7r * 60 = 5
Multiply through and simplify:
420r = 5
Divide each side by 5 to isolate r:
r = 1/84
So now we want to find out how many minutes it takes 10 people to paint 10 walls using this rate:
10rt = 10
With r = 1/84, we have:
10t/84 = 10
Cross multiply:
10t = 840
To solve for t, we t[URL='https://www.mathcelebrity.com/1unk.php?num=10t%3D840&pl=Solve']ype this equation into our search engine[/URL] and we get:
t = [B]84 minutes[/B]

Jack reads 90 pages of a book in six hours. What is the average number of pages he read each hour

Jack reads 90 pages of a book in six hours. What is the average number of pages he read each hour
90 pages / 6 hour = 90/6
Type [URL='https://www.mathcelebrity.com/fraction.php?frac1=90%2F6&frac2=3%2F8&pl=Simplify']90/6 in our search engine, click simplify[/URL], and we get:
[B]15 pages per hour[/B]

Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocola

Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.
If Jack had 2 chocolates left, then the total given to his friends is:
50 - 2 = 48
Let f be the number of friends at his birthday party. Then we have:
3f = 48
[URL='https://www.mathcelebrity.com/1unk.php?num=3f%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]f = 16[/B]

Jada scored 15 points in one basketball game and p points in another. Her two-game total is 34 point

Jada scored 15 points in one basketball game and p points in another. Her two-game total is 34 points
The phrase [I]total[/I] means a sum, so we have the following equation:
15 + p = 34
To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=15%2Bp%3D34&pl=Solve']type this equation into our search engine [/URL]and we get:
p = [B]19[/B]

James is four time as old as peter if their combined age is 30 how old is James.

James is four time as old as peter if their combined age is 30 how old is James.
Let j be Jame's age. Let p be Peter's age. We're given:
[LIST=1]
[*]j = 4p
[*]j + p = 30
[/LIST]
Substitute (1) into (2)
4p + p = 30
Combine like terms:
5p = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=5p%3D30&pl=Solve']Type 5p = 30 into our search engine[/URL], and we get p = 6.
Plug p = 6 into equation (1) to get James's age, we get:
j = 4(6)
j = [B]24[/B]

jamie needs 3 cups of flour and 4 cups of sugar how many cups of sugar will she need if she uses 9 c

jamie needs 3 cups of flour and 4 cups of sugar how many cups of sugar will she need if she uses 9 cups of flour?
Set up a proportion of flour/sugar:
3/4 = 9/x
[URL='http://www.mathcelebrity.com/prop.php?num1=3&num2=9&den1=4&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']Cross multiply or enter that into the search engine[/URL]
3x = 36
[B]x = 12[/B]

Jane did this calculation a. Add -12 b.subtract -9 c. Add 8 d. Subtract -2 the result is -5. What wa

Jane did this calculation a. Add -12 b.subtract -9 c. Add 8 d. Subtract -2 the result is -5. What was the original number?
Let the original number be n.
[LIST=1]
[*]Add -12: n - 12
[*]Subtract -9: n - 12 - -9 = n - 12 + 9
[*]Add 8: n - 12 + 9 + 8
[*]Subtract - 2: n - 12 + 9 + 8 - -2 = n - 12 + 9 + 8 + 2
[*]The result is -5. So we build the following equation:
[/LIST]
n - 12 + 9 + 8 + 2 = -5
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n-12%2B9%2B8%2B2%3D-5&pl=Solve']type it in our search engine[/URL] and we get:
[B]n = -12[/B]

Jane has $7.50 to spend in the candy store. She likes lollipops and gumballs. Each lollipop costs

Jane has $7.50 to spend in the candy store. She likes lollipops and gumballs. Each lollipop costs $2.75, and each gumball costs $0.50. If Jane decides to buy 1 lollipop, then what is the greatest number of gumballs Jane can buy? A
Subtract the cost of 1 lollipop:
$7.50 - $2.75 = $4.75
Let the number of gumballs = g. We have:
0.50g = $4.75
[URL='https://www.mathcelebrity.com/1unk.php?num=0.50g%3D4.75&pl=Solve']Run this through the search engine[/URL] to get g = 9.5 The problem asks for the greatest number. So we round down to [B]9 gumballs[/B].

Jason wrote a total of 8 pages over 2 hours. How many hours will Jason have to spend writing this we

Jason wrote a total of 8 pages over 2 hours. How many hours will Jason have to spend writing this week in order to have written a total of 12 pages? Assume the relationship is directly proportional.
Set up a proportion of pages to hours
8 pages/2 hours = 12 pages/x hours
enter 8/2 = 12/x into the [URL='http://www.mathcelebrity.com/prop.php?num1=8&num2=12&den1=2&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']search engine[/URL]:
[B]x = 3[/B]

Jennifer added $120 to her savings account during July. If this brought her balance to $700, how muc

Jennifer added $120 to her savings account during July. If this brought her balance to $700, how much has she saved previously?
We have a starting balance s. We're given:
s + 120 = 700
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B120%3D700&pl=Solve']type it in our search engine[/URL] and we get:
s = [B]580[/B]

Jennifer is playing cards with her bestie when she draws a card from a pack of 25 cards numbered fro

Jennifer is playing cards with her bestie when she draws a card from a pack of 25 cards numbered from 1 to 25. What is the probability of drawing a number that is square?
The squares from 1 - 25 less than or equal to 25 are as follows:
[LIST=1]
[*]1^2 = 1
[*]2^2 = 4
[*]3^2 = 9
[*]4^2 = 16
[*]5^2 = 25
[/LIST]
So the following 5 cards are squares:
{1, 4, 9, 16, 25}
Therefore, our probability of drawing a square is:
P(square) = Number of Squares / Number of Cards
P(square) = 5/25
This fraction can be simplified. So [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F25&frac2=3%2F8&pl=Simplify']we type in 5/25 into our search engine, choose simplify[/URL], and we get:
P(square) = [B]1/5[/B]

Jenny added $150 to her savings account in July. At the end if the month she had $500. How much did

Jenny added $150 to her savings account in July. At the end if the month she had $500. How much did she start with?
Let the starting balance be s. A deposit means we added 150 to s to get 500. We set up this equation below:
s + 150 = 500
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B150%3D500&pl=Solve']type this equation into our search engine[/URL] and we get:
s = 3[B]50[/B]

Jenny has $1200 and is spending $40 per week. Kelsey has $120 and is saving $50 a week. In how many

Jenny has $1200 and is spending $40 per week. Kelsey has $120 and is saving $50 a week. In how many weeks will Jenny and Kelsey have the same amount of money?
Jenny: Let w be the number of weeks. Spending means we subtract, so we set up a balance equation B(w):
B(w) = 1200 - 40w
Kelsey: Let w be the number of weeks. Saving means we add, so we set up a balance equation B(w):
B(w) = 120 + 50w
When they have the same amount of money, we set the balance equations equal to each other:
1200 - 40w = 120 + 50w
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=1200-40w%3D120%2B50w&pl=Solve']type this equation into our search engine[/URL] and we get:
w = [B]12[/B]

Jeremy can plant 10 trees in 4 hours. How many trees can he plant in 10 hours?

Jeremy can plant 10 trees in 4 hours. How many trees can he plant in 10 hours?
Set up a proportion of trees planted to hours where t is the number of trees planted in 10 hours.
10/4 = t/10
[URL='https://www.mathcelebrity.com/prop.php?num1=10&num2=t&den1=4&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']Type this expression into the search engine[/URL] and we get [B]t = 25[/B].
This means Jeremy can plant 25 trees in 10 hours.

Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82,

Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82, how old is the eldest of them
Let j be Jim's age, a be Alex's age, and u be June's age. We have 3 given equations:
[LIST=1]
[*]j + a + u = 82
[*]j = u + 9
[*]a = u - 8
[/LIST]
Substitute (2) and (3) into (1)
(u + 9) + (u - 8) + u = 82
Combine Like Terms:
3u + 1 = 82
[URL='https://www.mathcelebrity.com/1unk.php?num=3u%2B1%3D82&pl=Solve']Type this equation into the search engine[/URL], and we get u = 27.
The eldest (oldest) of the 3 is Jim. So we have from equation (2)
j = u + 9
j = 27 + 9
[B]j = 36[/B]

Jimmy was given $16 for washing the dog.He now has $47. How much money did he start with?

Jimmy was given $16 for washing the dog. He now has $47. How much money did he start with?
Let his starting money be s. We're told:
s + 16 = 47
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B16%3D47&pl=Solve']type this equation into our search engin[/URL]e and we get:
s = [B]31[/B]

Joaquin buys 3 dozen lightbulbs. After changing the lightbulbs in his house,he has 15 lightbulbs lef

Joaquin buys 3 dozen lightbulbs. After changing the lightbulbs in his house,he has 15 lightbulbs left. How many lightbulbs did he use?
[URL='https://www.mathcelebrity.com/quantcon.php?quant=3&pl=Calculate&type=dozen']Type 3 dozen into the search engine[/URL]. We get 36 units.
Now, if Joaquin has 15 lightbulbs left, we subtract 15 from 36: 36 - 15 = [B]21 lightbulbs used[/B]

Jody is buying a scrapbook and sheets of designer paper. She has $40 and needs at least $18.25 to bu

Jody is buying a scrapbook and sheets of designer paper. She has $40 and needs at least $18.25 to buy the scrapbook. Each sheet of paper costs $0.34. How many sheets of paper can she buy?
Set up a cost equation for the number of pieces of paper (p):
0.34p + 18.25 <= 40 <-- we have an inequality since we can't go over 40
[URL='https://www.mathcelebrity.com/1unk.php?num=0.34p%2B18.25%3C%3D40&pl=Solve']Type this inequality into our search engine[/URL] and we get:
p <= 63.97
We round down, so we get p = [B]63[/B].

Joe opens a bank account that starts with $20 and deposits $10 each week. Bria has a different accou

Joe opens a bank account that starts with $20 and deposits $10 each week. Bria has a different account that starts with $1000 but withdraws $15 each week. When will Joe and Bria have the same amount of money?
Let w be the number of weeks. Deposits mean we add money and withdrawals mean we subtract money.
[U]Joe's Balance function B(w) where w is the number of weeks:[/U]
20 + 10w
[U]Bria's Balance function B(w) where w is the number of weeks:[/U]
1000 - 15w
[U]The problem asks for when both balances will be the same. So we set them equal to each other and solve for w:[/U]
20 + 10w = 1000 - 15w
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=20%2B10w%3D1000-15w&pl=Solve']type this equation into our search engine[/URL] and we get:
w = 39.2
We round up to full week and get:
w = [B]40[/B]

John earns $5 mowing lawns. How many hours must he work to earn $40?

John earns $5 mowing lawns. How many hours must he work to earn $40?
Let hours worked be h. We have:
Earnings = Hourly Rate * Hours Worked
40 = 5h
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=40%3D5h&pl=Solve']type it in our search engine[/URL] and we get:
h = [B]8[/B]

Johnny Rocket can run 300 meters in 90 seconds. If his speed remains constant, how far could he ru

Johnny Rocket can run 300 meters in 90 seconds. If his speed remains constant, how far could he run in 500 seconds? Round to one decimal place.
Set up the distance equation:
Distance = Rate * Time
300 = 90r
Solving this equation for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=300%3D90r&pl=Solve']type it in our search engine[/URL] and we get:
r = 3.333
For 500 seconds, we set up our distance equation again:
Distance = 500 * 3.333333
Distance = [B]1666.7 meters[/B]

Jow buys 9 CD’s for the same price, and also a cassette tape for $9.45. His total bill was 118.89. W

Jow buys 9 CD’s for the same price, and also a cassette tape for $9.45. His total bill was 118.89. What was the cost of one CD?
Let the price of each cd be c. We're given the equation:
9c + 9.45 = 118.89
[URL='https://www.mathcelebrity.com/1unk.php?num=9c%2B9.45%3D118.89&pl=Solve']We type this equation into our search engine[/URL] and we get:
c = [B]12.16[/B]

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51
Let JP's age be j. Let Reyna's age be r. We're given two expressions:
[LIST=1]
[*]w = 2r
[*]r + w <= 51. ([I]Does not exceed means less than or equal to)[/I]
[/LIST]
We substitute (1) into (2) for w to get the inequality:
r + 2r <= 51
To solve this inequality, we type it in our search engine and we get:
[B]r <= 17[/B]

Julie has $300 to plan a dance. There is a one-time fee of $75 to reserve a room. It also costs $1.5

Julie has $300 to plan a dance. There is a one-time fee of $75 to reserve a room. It also costs $1.50 per person for food and drinks. What is the maximum number of people that can come to the dance?
Let each person be p. We have the following relationship for cost:
1.50p + 75 <=300
We use the <= sign since we cannot go over the $300 budget.
[URL='https://www.mathcelebrity.com/1unk.php?num=1.50p%2B75%3C%3D300&pl=Solve']We type this inequality into our search engine[/URL], and we get:
p <= 150
Since we have the equal sign within the inequality, the maximum number of people that can come to the dance is [B]150.[/B]

Karen earns $20 per hour and already has $400 saved, and wants to save $1200. How many hours until b

Karen earns $20 per hour and already has $400 saved, and wants to save $1200. How many hours until bob gets his $1200 goal?
Set up he savings function S(h) where h is the number of hours needed:
S(h) = savings per hour * h + current savings amount
S(h) = 20h + 400
The question asks for h when S(h) = 1200:
20h + 400 = 1200
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B400%3D1200&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]40[/B]

Karin has 3 to spend in the arcade. The game she likes costs 50c per play. What are the possible num

Karin has 3 to spend in the arcade. The game she likes costs 50c per play. What are the possible numbers of times that she can play?
[U]Let x = the number of games Karin can play with her money[/U]
0.5x = 3
[U]Divide each side by 0.5[/U]
[B]x = 6[/B]

Karmen just got hired to work at Walmart. She spent $15 on her new uniform and she gets paid $8 per

Karmen just got hired to work at Walmart. She spent $15 on her new uniform and she gets paid $8 per hour. Write an equation that represents how much money she profits after working for a certain number of hours. How many hours will she have to work for in order to buy a new snowboard ( which costs $450)
Her profit equation P(h) where h is the number of hours worked is:
[B]P(h) = 8h - 15[/B]
Note: [I]We subtract 15 as the cost of Karmen's uniform.
[/I]
Next, we want to see how many hours Karmen must work to buy a new snowboard which costs $450.
We set the profit equation equal to $450
8h - 15 = 450
[URL='https://www.mathcelebrity.com/1unk.php?num=8h-15%3D450&pl=Solve']Typing 8h - 15 = 450 into the search engine[/URL], we get h = 58.13. We round this up to 59 hours.

Kartek bought 86 pizzas for a school party. If there are 516 people at his school, how much pizza sh

Kartek bought 86 pizzas for a school party. If there are 516 people at his school, how much pizza should each person get?
Setup unit slices:
[URL='https://www.mathcelebrity.com/search.php?q=86%2F516']86 pizzas / 516 people[/URL] = [B]1/6 pizza per person[/B]

Kate spent 1 more than Lauren, and together they spent 5

Kate spent 1 more than Lauren, and together they spent 5.
Let k be the amount Kate spent, and l be the amount Lauren spent. We're given:
[LIST=1]
[*]k = l + 1
[*]k + l = 5
[/LIST]
Substitute (1) into (2):
(l + 1) + l = 5
Group like terms
2l + 1 = 5
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B1%3D5&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]l = 2[/B]
Plug this into Equation (1), we get:
k = 2 + 1
[B]k = 3
[/B]
Kate Spent 3, and Lauren spent 2

Kate spent at most $2.50 on apples and oranges. She bought 5 apples at $0.36 each. What is the most

Kate spent at most $2.50 on apples and oranges. She bought 5 apples at $0.36 each. What is the most She spent on oranges
[U]Assumptions and givens:[/U]
[LIST]
[*]Let a be the total cost of apples
[*]Let o be the total cost of oranges
[/LIST]
The phrase [I]at most[/I] means less than or equal to, so we have:
a + o <= 2.50
[U]Find the cost of apples (a)[/U]
a = price per apple * quantity of apples
a = 0.36 * 5
a = 1.8
Our new inequality with a = 1.8 is:
1.8 + o <= 2.50
[URL='https://www.mathcelebrity.com/1unk.php?num=1.8%2Bo%3C%3D2.50&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]o <= 0.7[/B]

keisha is babysitting at 8$ per hour to earn money for a car. So far she has saved $1300. The car th

keisha is babysitting at 8$ per hour to earn money for a car. So far she has saved $1300. The car that keisha wants to buy costs at least $5440. How many hours does Keisha need to babysit to earn enough to buy the car
Set up the Earning function E(h) where h is the number of hours Keisha needs to babysit:
E(h) = 8h + 1300
The question asks for h when E(h) is at least 5440. The phrase [I]at least[/I] means an inequality, which is greater than or equal to. So we have:
8h + 1300 >= 5440
To solve this inequality, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h%2B1300%3E%3D5440&pl=Solve']type it in our search engine[/URL] and we get:
h >= [B]517.5[/B]

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 a

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account.
Keith's balance is written as B(w) where w is the number of weeks passed since the beginning of summer. We have:
B(w) = 500 - 25w
The problem asks for B(w) = 200, so we set 500 - 25w = 200.
[URL='https://www.mathcelebrity.com/1unk.php?num=500-25w%3D200&pl=Solve']Typing 500 - 25w = 200 into the search engine[/URL], we get [B]w = 12[/B].

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 a

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account
Our account balance is:
500 - 25w where w is the number of weeks.
We want to know the following for w:
500 - 25w = 200
[URL='https://www.mathcelebrity.com/1unk.php?num=500-25w%3D200&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 12[/B]

Keith is going to Renaissance Festival with $120 to pay for his admission, food and the cost of game

Keith is going to Renaissance Festival with $120 to pay for his admission, food and the cost of games. He spends a total of $85 on admission and food. Games cost $5 each. Which inequality models the maximum number of games Keith can play.
Let the number of games be g. Keith can spend less than or equal to 120. So we have
[B]5g + 85 <= 120
[/B]
If we want to solve the inequality for g, we [URL='https://www.mathcelebrity.com/1unk.php?num=5g%2B85%3C%3D120&pl=Solve']type it in our search engine[/URL] and we have:
g <= 7

Kellie has only $5.25 to buy breakfast. She wants to buy as many carrot muffins as she can. Each muf

Kellie has only $5.25 to buy breakfast. She wants to buy as many carrot muffins as she can. Each muffin costs $0.75. What’s an equation?
Let m be the number of muffins. Cost equals price * quantity, so we have:
[B]0.75m = 5.25
[/B]
To solve the equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.75m%3D5.25&pl=Solve']type the equation into our search engine[/URL] and we get:
m = [B]7[/B]

Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How

Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How old are they?
Let k be Kendra's age, m be Morgan's age, and l be Lizzie's age. We're given:
[LIST=1]
[*]k = 0.5m
[*]k = l - 3
[*]k + l + m = 39
[/LIST]
Rearranging (1) by multiplying each side by 2, we have:
m = 2k
Rearranging (2) by adding 3 to each side, we have:
l = k + 3
Substituting these new values into (3), we have:
k + (k + 3) + (2k) = 39
Group like terms:
(k + k + 2k) + 3 = 39
4k + 3 = 39
[URL='https://www.mathcelebrity.com/1unk.php?num=4k%2B3%3D39&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]k = 9
[/B]
Substitute this back into (1), we have:
m = 2(9)
[B]m = 18
[/B]
Substitute this back into (2), we have:
l = (9) + 3
[B][B]l = 12[/B][/B]

kim and jason just had business cards made. kim’s printing company charged a one time setup fee of $

kim and jason just had business cards made. kim’s printing company charged a one time setup fee of $8 and then $20 per box of cards. jason,meanwhile ordered his online. they cost $8 per box. there was no setup fee, but he had to pay $20 to have his order shipped to his house. by coincidence, kim and jason ended up spending the same amount on their business cards. how many boxes did each buy? how much did each spend?
Set up Kim's cost function C(b) where b is the number of boxes:
C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee
C(b) = 20c + 8 + 0
Set up Jason's cost function C(b) where b is the number of boxes:
C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee
C(b) = 8c + 0 + 20
Since Kim and Jason spent the same amount, set both cost equations equal to each other:
20c + 8 = 8c + 20
[URL='https://www.mathcelebrity.com/1unk.php?num=20c%2B8%3D8c%2B20&pl=Solve']Type this equation into our search engine[/URL] to solve for c, and we get:
c = 1
How much did they spend? We pick either Kim's or Jason's cost equation since they spent the same, and plug in c = 1:
Kim:
C(1) = 20(1) + 8
C(1) = 20 + 8
C(1) = [B]28
[/B]
Jason:
C(1) = 8(1) + 20
C(1) = 8 + 20
C(1) = [B]28[/B]

kim wants to buy candy for 4 dollars a pound. if she wants to spend less than 20 dollars, how many b

kim wants to buy candy for 4 dollars a pound. if she wants to spend less than 20 dollars, how many bags can she buy
Since cost = price * quantity, we have the following inequality with b as the number of bags:
4b < 20
To solve this inequality for b, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4b%3C20&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]b < 5[/B]

Lauren's savings increased by 12 and is now 31

Lauren's savings increased by 12 and is now 31
[LIST]
[*]Let Lauren's savings be s.
[*]The phrase increased by means we add.
[*]The phrase [I]is now[/I] means an equation.
[*]We have an algebraic expression of:
[/LIST]
[B]s + 12 = 31
[/B]
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B12%3D31&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]19[/B]

Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI

Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI with the following monthly billing policies. Each company's monthly billing policy has an initial operating fee and charge per megabyte.
Operating Fee charge per Mb
CIVSIN 29.95 0.14
GOMI 4.95 0.39
(i) Write down a system of equations to model the above situation
(ii) At how many Mb is the monthly cost the same? What is the equal monthly cost of the two plans?
(i) Set up a cost function C(m) for CIVSIN where m is the number of megabytes used:
C(m) = charge per Mb * m + Operating Fee
[B]C(m) = 0.14m + 29.95[/B]
Set up a cost function C(m) for GOMI where m is the number of megabytes used:
C(m) = charge per Mb * m + Operating Fee
[B]C(m) = 0.39m + 4.95
[/B]
(ii) At how many Mb is the monthly cost the same?
Set both cost functions equal to each other:
0.14m + 29.95 = 0.39m + 4.95
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B29.95%3D0.39m%2B4.95&pl=Solve']type this equation into our search engine[/URL] and we get:
m = [B]100[/B]
(ii) What is the equal monthly cost of the two plans?
CIVSIN - We want C(100) from above where m = 100
C(100) = 0.14(100) + 29.95
C(100) = 14 + 29.95
C(100) = [B]43.95[/B]
GOMI - We want C(100) from above where m = 100
C(100) = 0.39(100) + 4.95
C(100) = 39 + 4.95
C(100) = [B]43.95[/B]

Linda estimates that her business is growing at a rate of 6% per year. Her profits is 2002 were $30,

Linda estimates that her business is growing at a rate of 6% per year. Her profits is 2002 were $30,000. To the nearest hundred dollars, estimate her profits for 2011.
Calculate the number of years of appreciation:
Appreciation years = 2011 - 2002
Appreciation years = 9
So we want 30000 to grow for 9 years at 6%. We [URL='https://www.mathcelebrity.com/apprec-percent.php?num=30000togrowfor9yearsat6%.whatisthevalue&pl=Calculate']type this into our search engine[/URL] and we get:
[B]$50,684.37[/B]

Lindsey took a total of 8 quizzes over the course of 2 weeks. After attending 5 weeks of school this

Lindsey took a total of 8 quizzes over the course of 2 weeks. After attending 5 weeks of school this quarter, how many quizzes will Lindsey have taken in total? Assume the relationship is directly proportional.
Since the relationship is directly proportional, set up a proportion of quizzes to weeks, where q is the number of quizzes Lindsey will take in 5 weeks:
8/2 = q/5
[URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=q&den1=2&den2=5&propsign=%3D&pl=Calculate+missing+proportion+value']We type this proportion into our search engine[/URL], and we get:
[B]q = 20
[/B]
Another way to look at this is, Lindsey takes 8 quizzes over 2 weeks. This means she takes 4 per week since 8/2 = 4.
So if she takes 4 quizzes per week, then in 5 weeks, she takes 4*5 = 20 quizzes.

Line m passes through points (3, 16) and (8, 10). Line n is perpendicular to m. What is the slope of

Line m passes through points (3, 16) and (8, 10). Line n is perpendicular to m. What is the slope of line n?
First, find the slope of the line m passing through points (3, 16) and (8, 10).
[URL='https://www.mathcelebrity.com/slope.php?xone=3&yone=16&slope=+2%2F5&xtwo=8&ytwo=10&pl=You+entered+2+points']Typing the points into our search engine[/URL], we get a slope of:
m = -6/5
If line n is perpendicular to m, then the slope of n is denote as:
n = -1/m
n = -1/-6/5
n = -1*-5/6
n = [B]5/6[/B]

Lisa has $150 at most to spend on clothes. She wants to buy a pair of jeans for $58 and will spend t

Lisa has $150 at most to spend on clothes. She wants to buy a pair of jeans for $58 and will spend the rest on t-shirts that cost $14 each.
Let the number of t-shirts be t. Lisa can spend up to, but not more than 150. We have the following inequality:
14t + 58 <= 150
To solve this inequality, we [URL='https://www.mathcelebrity.com/1unk.php?num=14j%2B58%3C%3D150&pl=Solve']type it in our search engine[/URL] and we get:
t <= 6.57
To round to a whole number, we round down to [B]t = 6 [/B]

Local salesman receives a base salary of $650 monthly. He also receives a commission of 11% on all s

Local salesman receives a base salary of $650 monthly. He also receives a commission of 11% on all sales over $1500. How much would he have to sell in one month if he needed to have $3000
Let the Sales amount be s. We have:
Sales over 1,500 is written as s - 1500
11% is also 0.11 as a decimal, so we have:
0.11(s - 1500) + 650 = 3000
Multiply through:
0.11s - 165 + 650 = 3500
0.11s + 485 = 3500
To solve this equation for s, [URL='https://www.mathcelebrity.com/1unk.php?num=0.11s%2B485%3D3500&pl=Solve']we type it in our search engine[/URL] and we get:
s = [B]27,409.10[/B]

Logan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nep

Logan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nephew?
Let the age of Logan's nephew be n. We're given:
4n + 8 = 32 (Since [I]older[/I] means we add)
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=4n%2B8%3D32&pl=Solve']type it into our search engine[/URL] and we get:
[B]n = 6[/B]

Lorda is older than Kate. The sum of their ages is 30. The difference in their ages is 6. What are t

Lorda is older than Kate. The sum of their ages is 30. The difference in their ages is 6. What are their ages?
Let Lorda's age be l. Let Kate's age be k. We're given two equations:
[LIST=1]
[*]l + k = 30
[*]l - k = 6 <-- Since Lorda is older
[/LIST]
Add the 2 equations together and we eliminate k:
2l = 36
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%3D36&pl=Solve']Typing this equation into our search engine[/URL] and solving for l, we get:
l = [B]18[/B]
Now substitute l = 18 into equation 1:
18 + k = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=18%2Bk%3D30&pl=Solve']Type this equation into our search engine[/URL] and solving for k, we get:
k = [B]12[/B]

Mackenzie baked 12 cookies with 2 scoops of flour. How many scoops of flour does Mackenzie need in o

Mackenzie baked 12 cookies with 2 scoops of flour. How many scoops of flour does Mackenzie need in order to bake 18 cookies? Assume the relationship is directly proportional.
Set up a proportion of cookies to scoops with s as the number of scoops needed for 18 cookies:
12/2 = 18/s
To solve for s, we [URL='https://www.mathcelebrity.com/prop.php?num1=12&num2=18&den1=2&den2=s&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search engine[/URL] and we get:
s = [B]3
[/B]

Maggie earns $10 each hour she works at the pet store and $0.25 for each phone call she answers. Mag

Maggie earns $10 each hour she works at the pet store and $0.25 for each phone call she answers. Maggie answered 60 phone calls and earned $115 last week
Set up an equation where c is the number of phone calls Maggie answers and h is the number of hours Maggie worked:
0.25c + 10h = 115
We're given c = 60, so we have:
0.25(60) + 10h = 115
15 + 10h = 115
We want to solve for h. So we[URL='https://www.mathcelebrity.com/1unk.php?num=15%2B10h%3D115&pl=Solve'] type this equation into our search engine[/URL] and we get:
h = [B]10[/B]

maggie has two job offers. The first job offers to pay her $50 per week and 10 1/2 cents per flier.

maggie has two job offers. The first job offers to pay her $50 per week and 10 1/2 cents per flier. The second job offer will pay only $30 per week but gives 20 cents per flier. Write and solve an equation to find how many fliers must she deliver so that the two offers pay the same per week?
Let the number of fliers be f.
First job:
0.105f + 50
Second job:
20f + 30
Set them equal to each other:
0.105f + 50 = 20f + 30
[URL='https://www.mathcelebrity.com/1unk.php?num=0.105f%2B50%3D20f%2B30&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]f = 1[/B]

Marcela is having a presidential debate watching party with all of her friends, She will be making c

Marcela is having a presidential debate watching party with all of her friends, She will be making chicken wings and hot dogs. Each chicken wing costs $2 to make and each hot dog costs $3. She needs to spend at least $500. Marcela knows that she will make more than 50 chicken wings and hot dogs combined. She also knows that she will make less than 120 chicken wings and less that 100 hot dogs. What are her inequalities?
Let c be the number of chicken wings and h be the number of hot dogs. Set up the given inequalities:
[LIST=1]
[*]c + h > 50 [I]Marcela knows that she will make more than 50 chicken wings and hot dogs combined.[/I]
[*]2c + 3h >= 500 [I]She needs to spend at least $500[/I]
[*]c < 120 [I]She also knows that she will make less than 120 chicken wings[/I]
[*]h < 100 [I]and less that 100 hot dogs[/I]
[/LIST]

Marco orders a large pizza, with a diameter of 14 inches. It is cut into 8 congruent pieces. what is

Marco orders a large pizza, with a diameter of 14 inches. It is cut into 8 congruent pieces. what is the area of one piece?
A pizza is a circle. If the diameter of the pizza is 14 inches, the radius is 14/2 = 7 inches.
Area of a circle is pi(r^2). With r = 7, we have:
A =7^2(pi)
A = 49pi
Area of a slice of pizza is the area of the full pizza divided by 8
A(Slice) = [B]49pi/8[/B]

Marco puts his coins into stacks. Each stack has 10 coins. He makes 17 stacks of quarters. He makes

Marco puts his coins into stacks. Each stack has 10 coins. He makes 17 stacks of quarters. He makes 11 stacks of dimes. He makes 8 stacks of nickels. How much money does Marco have in his stacks of coins?
[U]Value of Quarters:[/U]
Quarter Value = Value per quarter * coins per stack * number of stacks
Quarter Value = 0.25 * 10 * 17
Quarter Value = 42.5
[U]Value of Dimes:[/U]
Dime Value = Value per dime * coins per stack * number of stacks
Dime Value = 0.10 * 10 * 11
Dime Value = 11
[U]Value of Nickels:[/U]
Nickel Value = Value per nickel * coins per stack * number of stacks
Nickel Value = 0.05 * 10 * 8
Nickel Value = 4
[U]Calculate total value of Marco's coin stacks[/U]
Total value of Marco's coin stacks = Quarter Value + Dime Value + Nickel Value
Total value of Marco's coin stacks = 42.5 + 11 + 4
Total value of Marco's coin stacks = [B]57.5[/B]

Marco takes 2 quizzes each week. Write an equation that shows the relationship between the number of

Marco takes 2 quizzes each week. Write an equation that shows the relationship between the number of weeks x and the total number of quizzes y. Write your answer as an equation with y first, followed by an equals sign.
Our total quizzes equal 2 times the number of weeks (x):
[B]y = 2x[/B]

Marcus drives a machine that paints lines along the highway. He needs to paint a line that is 9/10 o

Marcus drives a machine that paints lines along the highway. He needs to paint a line that is 9/10 of a mile long. He is 2/3 of the way done when he runs out of paint. What fraction of a mile has he painted?
Marcus has painted 2/3 of 9/10.
If we [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F3&frac2=9%2F10&pl=Multiply']type 2/3 of 91/20 in our search engine[/URL], we get:
[B]3/5[/B]

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. How many did she start with?
Take this in parts
[LIST=1]
[*]Maria starts with b boxes.
[*]She buys seven more. So she has b + 7 boxes
[*]A week later, half of all her boxes are destroyed in a fire. Which means she's left with 1/2. (b + 7)/2
[*]Now she has 22 boxes. So we set (b + 7)/2 = 22
[/LIST]
(b + 7)/2 = 22
Cross multiply:
b + 7 = 22 * 2
b + 7 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B7%3D44&pl=Solve']Typing this equation into our search engine and solving for b[/URL], we get:
[B]b = 37[/B]

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now

Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start?
Let the number of boxes Maria started with be b. We're given the following pieces:
[LIST]
[*]She starts with b
[*]She bought 7 boxes. So we add 7 to b: b + 7
[*]If half the boxes were destroyed, she's left with 1/2. So we divide (b + 7)/2
[*]Only 22 boxes left means we set (b + 7)/2 equal to 22
[/LIST]
(b + 7)/2 = 22
Cross multiply:
b + 7 = 22 * 2
b + 7 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B7%3D44&pl=Solve']Type this equation into our search engine[/URL] to solve for b and we get:
b = [B]37[/B]

Maria is saving money to buy a bike that cost 133$. She has 42$ and will save an additional 7 each w

Maria is saving money to buy a bike that cost 133$. She has 42$ and will save an additional 7 each week.
Set up an equation with w as the number of weeks. We want to find w such that:
7w + 42 = 133
[URL='https://www.mathcelebrity.com/1unk.php?num=7w%2B42%3D133&pl=Solve']Typing this equation into our search engine[/URL], we get:
w = [B]13[/B]

Marion Middle School has 600 students. Mike surveys a random sample of 30 students and finds that 7

Marion Middle School has 600 students. Mike surveys a random sample of 30 students and finds that 7 of them play a musical instrument. How many students at the school are likely to play a musical instrument?
Set up a proportion of those that play musical instruments to total students where m is the amount of students in the 600 who play a musical instrument:
7/30 = m/600
[URL='https://www.mathcelebrity.com/prop.php?num1=7&num2=m&den1=30&den2=600&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
m = [B]140[/B]

Mark and Jennie are bowling. Jennie’s score is double Mark’s score. If the sum of their score is 171

Mark and Jennie are bowling. Jennie’s score is double Mark’s score. If the sum of their score is 171, find each person’s score by writing out an equation.
Let Mark's score be m. Let Jennie's score be j. We're given two equations:
[LIST=1]
[*]j = 2m
[*]j + m = 171
[/LIST]
Substitute equation (1) into equation (2):
2m + m = 171
[URL='https://www.mathcelebrity.com/1unk.php?num=2m%2Bm%3D171&pl=Solve']Type this equation into our search engine[/URL] to solve for m:
m = [B]57
[/B]
To solve for j, we substitute m = 57 in equation (1) above:
j = 2(57)
j = [B]114[/B]

Marla wants to rent a bike Green Lake Park has an entrance fee of $8 and charges $2 per hour for bik

Marla wants to rent a bike Green Lake Park has an entrance fee of $8 and charges $2 per hour for bike Oak Park has an entrance fee of $2 and charges $5 per hour for bike rentals she wants to know how many hours are friend will make the costs equal
[U]Green Lake Park: Set up the cost function C(h) where h is the number of hours[/U]
C(h) = Hourly Rental Rate * h + Entrance Fee
C(h) = 2h + 8
[U]Oak Park: Set up the cost function C(h) where h is the number of hours[/U]
C(h) = Hourly Rental Rate * h + Entrance Fee
C(h) = 5h + 2
[U]Marla wants to know how many hours make the cost equal, so we set Green Lake Park's cost function equal to Oak Parks's cost function:[/U]
2h + 8 = 5h + 2
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2h%2B8%3D5h%2B2&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]2[/B]

Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find t

Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find the ages of Martha and Harry.
Let m be Martha's age. Let h be Harry's age. We're given two equations:
[LIST=1]
[*]m = h + 18 [I](older means we add)[/I]
[*]h + m = 106
[/LIST]
Substitute equation (1) into equation (2) for m:
h + h + 18 = 106
To solve for h, [URL='https://www.mathcelebrity.com/1unk.php?num=h%2Bh%2B18%3D106&pl=Solve']we type this equation into our search engine[/URL] and we get:
h = [B]44[/B]

Martha's age 2/3 of her brother's age. Martha is 24 years old now. How old is her brother?

Martha's age 2/3 of her brother's age. Martha is 24 years old now. How old is her brother?
Let her brother's age be b. We're given:
2b/3 = 24
To solve this proportion for b, [URL='https://www.mathcelebrity.com/prop.php?num1=2b&num2=24&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
b = [B]36[/B]

Mary went bowling on the weekend. Each game cost $2.50, and the shoe rental $2.00. She spent $14.50

Mary went bowling on the weekend. Each game cost $2.50, and the shoe rental $2.00. She spent $14.50 total. How many games did she bowl?
Set up the equation where g is the number of games. We add the shoe rental fee to the cost per games
2.5g + 2 = 14.50
To solve for g, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5g%2B2%3D14.50&pl=Solve']type this equation into our search engine[/URL] and we get:
g = [B]5[/B]

Matt has $100 dollars in a checking account and deposits $20 per month. Ben has $80 in a checking ac

Matt has $100 dollars in a checking account and deposits $20 per month. Ben has $80 in a checking account and deposits $30 per month. Will the accounts ever be the same balance? explain
Set up the Balance account B(m), where m is the number of months since the deposit.
Matt:
B(m) = 20m + 100
Ben:
B(m) = 80 + 30m
Set both balance equations equal to each other to see if they ever have the same balance:
20m + 100 = 80 + 30m
To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=20m%2B100%3D80%2B30m&pl=Solve']we type this equation into our search engine[/URL] and we get:
m = [B]2
So yes, they will have the same balance at m = 2[/B]

Max is 23 years younger than his father.Together their ages add up to 81.

Max is 23 years younger than his father.Together their ages add up to 81.
Let Max's age be m, and his fathers' age be f. We're given:
[LIST=1]
[*]m = f - 23 <-- younger means less
[*]m + f = 81
[/LIST]
Substitute Equation (1) into (2):
(f - 23) + f = 81
Combine like terms to form the equation below:
2f - 23 = 81
[URL='https://www.mathcelebrity.com/1unk.php?num=2f-23%3D81&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]f = 52[/B]
Substitute this into Equation (1):
m = 52 - 23
[B]m = 29[/B]

Max's age is 2 more than his fathers age divided by 4. Max is 13 years old. How old is his dad?

Max's age is 2 more than his fathers age divided by 4. Max is 13 years old. How old is his dad?
Let Max's father be age f. We're given:
(f + 2)/4 = 13
Cross Multiply:
f + 2 = 52
[URL='https://www.mathcelebrity.com/1unk.php?num=f%2B2%3D52&pl=Solve']Typing this equation into the search engine[/URL], we get:
f = [B]50[/B]

Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many

Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many weeks will megan and connor have saved the same amount
[U]Set up the Balance function B(w) where w is the number of weeks for Megan:[/U]
B(w) = savings per week * w + Current Balance
B(w) = 5.50w + 50
[U]Set up the Balance function B(w) where w is the number of weeks for Connor:[/U]
B(w) = savings per week * w + Current Balance
B(w) = 7.75w + 18.50
The problem asks for w when both B(w) are equal. So we set both B(w) equations equal to each other:
5.50w + 50 = 7.75w + 18.50
To solve this equation for w, we[URL='https://www.mathcelebrity.com/1unk.php?num=5.50w%2B50%3D7.75w%2B18.50&pl=Solve'] type it in our search engine[/URL] and we get:
w = [B]14[/B]

Meryl can only take 4 out of 7 classes offered during the summer. How many different ways can she ch

Meryl can only take 4 out of 7 classes offered during the summer. How many different ways can she choose the classes she will take
We want 7 choose 4, or 7C4:
We [URL='https://www.mathcelebrity.com/permutation.php?num=7&den=4&pl=Combinations']type 7C4 into our search engine and we get[/URL]:
35

Miguel has $80 in his bank and saves $2 a week. Jesse has $30 in his bank but saves $7 a week. In ho

Miguel has $80 in his bank and saves $2 a week. Jesse has $30 in his bank but saves $7 a week. In how many weeks will Jesse have more in his bank than Miguel?
[U]Set up the Bank value B(w) for Miguel where w is the number of weeks[/U]
B(w) = Savings Per week * w + Current Bank Balance
B(w) = 2w + 80
[U]Set up the Bank value B(w) for Jesse where w is the number of weeks[/U]
B(w) = Savings Per week * w + Current Bank Balance
B(w) = 7w + 30
The problem asks when Jesse's account will be more than Miguel's. So we set up an inequality where:
7w + 30 > 2w + 80
To solve this inequality, we [URL='https://www.mathcelebrity.com/1unk.php?num=7w%2B30%3E2w%2B80&pl=Solve']type it in our search engine[/URL] and we get:
[B]w > 10[/B]

Mike cut 2 acres of grass in 30 minutes on his tractor. Which proportion would determine how many ac

Mike cut 2 acres of grass in 30 minutes on his tractor. Which proportion would determine how many acres of grass Mike cut in 60 minutes?
Let a be the number of acres of grass cut by Mike in 60 minutes. We have the following proportion:
2/30 = a/60
[URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=a&den1=30&den2=60&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this problem into our search engine[/URL], we get [B]a = 4[/B].

mike went to canalside with $40 to spend. he rented skates for $10 and paid $3 per hour to skate.wha

mike went to canalside with $40 to spend. he rented skates for $10 and paid $3 per hour to skate.what is the greatest number of hours Mike could have skated?
Let h be the number of hours of skating. We have the cost function C(h):
C(h) = Hourly skating rate * h + rental fee
C(h) = 3h + 10
The problem asks for h when C(h) = 40:
3h + 10 = 40
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=3h%2B10%3D40&pl=Solve']type it in our search engine[/URL] and we get:
h = [B]10[/B]

Molly is making strawberry infused water. For each ounce of strawberry juice, she uses two times as

Molly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water as juice. How many ounces of strawberry juice and how many ounces of water does she need to make 40 ounces of strawberry infused water?
Let j be the ounces of strawberry juice and w be the ounces of water. We're given:
[LIST=1]
[*]j + w = 40
[*]w = 3j
[/LIST]
Substitute (2) into (1):
j + 3j = 40
Combine like terms:
4j = 40
[URL='https://www.mathcelebrity.com/1unk.php?num=4j%3D40&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]j = 10[/B]
From equation (2), we substitute j = 2:
w = 3(10)
[B]w = 30
[/B]
This means we have [B]10 ounces of juice[/B] and [B]30 ounces of water[/B] for a 40 ounce mix.

Months with 31 days as set M

Months with 31 days as set M
Our cardinality of this set is 7, as show below:
{[B]January, March, May, July, August, October, December[/B]}

Mr turner sent his car to the workshop for repair work as well as to change 4 tires. Mr turner paid

Mr turner sent his car to the workshop for repair work as well as to change 4 tires. Mr turner paid $1035 in all. The repair work cost 5 times the price of each tire. The mechanic told Mr. turner that the repair work cost $500. Explain the mechanic’s mistake
Let the cost for work be w. Let the cost for each tire be t. We're given;
[LIST=1]
[*]w = 5t
[*]w + 4t = 1035
[/LIST]
Substitute equation 1 into equation 2:
(5t) + 4t = 1035
[URL='https://www.mathcelebrity.com/1unk.php?num=%285t%29%2B4t%3D1035&pl=Solve']Type this equation into our search engine[/URL], and we get:
t = 115
Substitute this into equation (1):
w = 5(115)
w = [B]575[/B]
The mechanic underestimated the work cost.

Mr. Demerath has a large collection of Hawaiian shirts. He currently has 42 Hawaiian shirts. He gets

Mr. Demerath has a large collection of Hawaiian shirts. He currently has 42 Hawaiian shirts. He gets 2 more every month. After how many months will Mr. Demerath have at least 65 Hawaiian shirts?
We set up the function H(m) where m is the number of months that goes by. Mr. Demerath's shirts are found by:
H(m) = 2m + 42
The problem asks for m when H(m) = 65. So we set H(m) = 65:
2m + 42 = 65
To solve this equation for m, we[URL='https://www.mathcelebrity.com/1unk.php?num=2m%2B42%3D65&pl=Solve'] type it in our search engine [/URL]and we get:
m = [B]11.5[/B]

Mrs. Lowe charges $45 an hour with a $10 flat fee for tutoring. Mrs. Smith charges $40 an hour wit

Mrs. Lowe charges $45 an hour with a $10 flat fee for tutoring. Mrs. Smith charges $40 an hour with a $15 flat fee to tutor. Write an equation that represents the situation when the cost is the same to be tutored by Mrs. Lowe and Mrs. Smith.
[U]Set up cost equation for Mrs. Lowe where h is the number of hours tutored:[/U]
Cost = Hourly Rate * number of hours + flat fee
Cost = 45h + 10
[U]Set up cost equation for Mrs. Smith where h is the number of hours tutored:[/U]
Cost = Hourly Rate * number of hours + flat fee
Cost = 40h + 15
[U]Set both cost equations equal to each other:[/U]
45h + 10 = 40h + 15 <-- This is our equation
To solve for h if the problem asks, we [URL='https://www.mathcelebrity.com/1unk.php?num=45h%2B10%3D40h%2B15&pl=Solve']type this equation into our search engine[/URL] and we get:
h = 1

Multiply 0 by 3 and add 4

Multiply 0 by 3 and add 4
multiply 0 by 3:
0 * 3
Then add 4:
[B]0 * 3 + 4 <--- [/B][I]This is our algebraic expression.[/I]
If we want to evaluate this expression, we [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=0%2A3%2B4&pl=Perform+Order+of+Operations']type it in our search engine[/URL] and we get:
[B]4[/B]

Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and su

Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and subtracting 4. Find the number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
multiply a number by 6 and subtract 6:
6x - 6
Multiply a number by 3 and subtract 4:
3x - 4
The phrase [I]gives the same result[/I] means an equation. So we set 6x - 6 equal to 3x - 4
6x - 6 = 3x - 4
To solve this equation for x, we type it in our search engine and we get:
x = [B]2/3[/B]

Multiplying a number by 6 is equal to the number increased by 9

Multiplying a number by 6 is equal to the number increased by 9.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Multiply it by 6 --> 6x
We set this equal to the same number increased by 9. Increased by means we add:
[B]6x = x + 9 <-- This is our algebraic expression
[/B]
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x%3Dx%2B9&pl=Solve']type it into the search engine [/URL]and get x = 1.8.

My brother is x years old. I am 5 years older than him. Our combined age is 30 years old. How old is

My brother is x years old. I am 5 years older than him. Our combined age is 30 years old. How old is my brother
Brother's age is x:
I am 5 years older, meaning I'm x + 5:
The combined age is found by adding:
x + (x + 5) = 30
Group like terms:
2x + 5 = 30
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B5%3D30&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]12.5[/B]

My rent was 800.00 a month. My landlord raised my rent to 1,240.00. What percentage did he raise m

My rent was 800.00 a month. My landlord raised my rent to 1,240.00. What percentage did he raise my rent?.
First, calculate the difference between the old and new rent:
Difference = 1,240 - 800 = 440
Percentage increase = 440/800
[URL='https://www.mathcelebrity.com/perc.php?num=440&den=800&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Type 440/800 into the search engine, and choose the percent option[/URL]
You get [B]55%[/B] increase.

MySQL Function List

A Search Engine with definitions on MySQL functions used to query

n and m are congruent and supplementary. prove n and m are right angles

n and m are congruent and supplementary. prove n and m are right angles
Given:
[LIST]
[*]n and m are congruent
[*]n and m are supplementary
[/LIST]
If n and m are supplementary, that means we have the equation:
m + n = 180
We're also given n and m are congruent, meaning they are equal. So we can substitute n = m into the supplementary equation:
m + m = 180
To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%3D180&pl=Solve']we type it in our search engine[/URL] and we get:
m = 90
This means m = 90, n = 90, which means they are both right angles since by definition, a right angle is 90 degrees.

Nancy shot a 16 on 4 holes of golf. At this rate, what can she expect her score to be if she plays 1

Nancy shot a 16 on 4 holes of golf. At this rate, what can she expect her score to be if she plays 18 holes? Round to the nearest whole number
Set up a proportion of score to holes of golf where s is the score for 18 holes:
16/4 = s/18
To solve this proportion for s, we [URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=s&den1=4&den2=18&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
s = [B]72[/B]

Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and i

Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and is spending $15 a week. [I]When will they both have the same amount of money in the bank?[/I]
[I][/I]
Set up the Account equation A(w) where w is the number of weeks that pass.
Nancy (we add since savings means she accumulates [B]more[/B]):
A(w) = 25w + 435
Shane (we subtract since spending means he loses [B]more[/B]):
A(w) = 875 - 15w
Set both A(w) equations equal to each other to since we want to see what w is when the account are equal:
25w + 435 = 875 - 15w
[URL='https://www.mathcelebrity.com/1unk.php?num=25w%2B435%3D875-15w&pl=Solve']Type this equation into our search engine to solve for w[/URL] and we get:
w =[B] 11[/B]

Nava is 17 years older than Edward. the sum of Navas age and Edwards ages id 29. How old is Nava?

Nava is 17 years older than Edward. the sum of Navas age and Edwards ages id 29. How old is Nava?
Let Nava's age be n and Edward's age be e. We have 2 equations:
[LIST=1]
[*]n = e + 17
[*]n + e = 29
[/LIST]
Substitute (1) into (2)
(e + 17) + e = 29
Group like terms:
2e + 17 = 29
Running this equation [URL='http://www.mathcelebrity.com/1unk.php?num=2e%2B17%3D29&pl=Solve']through our search engine[/URL], we get:
e = 6
Substitute this into equation (1)
n = 6 + 17
[B]n = 23[/B]

Nick said that his sister is 4 times as old as his brother, and together their ages add to 20 comple

Nick said that his sister is 4 times as old as his brother, and together their ages add to 20 complete this equation to find his brothers age
Let b be the brother's age and s be the sister's age. We're given two equations:
[LIST=1]
[*]s =4b
[*]b + s = 20
[/LIST]
Plug (1) into (2):
b + 4b = 20
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B4b%3D20&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]b = 4[/B]

Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years?

Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years?
Let n be Nicole's age. Let d be Donald's age. We're given two equations:
[LIST=1]
[*]n = 0.5d
[*]n + d = 72
[/LIST]
Substitute equation (1) into (2):
0.5d + d = 72
1.5d = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=1.5d%3D72&pl=Solve']Typing this equation into the search engine and solving for d[/URL], we get:
d = [B]48[/B]

Number of cents in q quarters is 275

Number of cents in q quarters is 275
Each quarter makes 25 cents. We write this as 0.25q.
Now set this equal to 275
0.25q = 275
Typing this [URL='http://www.mathcelebrity.com/1unk.php?num=0.25q%3D275&pl=Solve']equation in the search engine[/URL], we get [B]q = 1,100[/B].

Number Property

This calculator determines if an integer you entered has any of the following properties:

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

numerator of a fraction is 5 less than its denominator. if 1 is added to the numerator and to the de

numerator of a fraction is 5 less than its denominator. if 1 is added to the numerator and to the denominator the new fraction is 2/3. find the fraction.
Let n be the numerator.
Let d be the denominator.
We're given 2 equations:
[LIST=1]
[*]n = d - 5
[*](n + 1)/(d + 1) = 2/3
[/LIST]
Substitute equation (1) into equation (2) for n:
(d - 5 + 1) / (d + 1) = 2/3
(d - 4) / (d + 1) = 2/3
Cross multiply:
3(d - 4) = 2(d + 1)
To solve this equation for d, we type it in our search engine and we get:
d = 14
Substitute d = 14 into equation (1) to solve for n:
n = 14 - 5
n = 9
Therefore, our fraction n/d is:
[B]9/14[/B]

Oceanside Bike Rental Shop charges $15.00 plus $9.00 per hour for renting a bike. Dan paid $51.00 to

Oceanside Bike Rental Shop charges $15.00 plus $9.00 per hour for renting a bike. Dan paid $51.00 to rent a bike. How many hours was he hiking for?
Set up the cost equation C(h) where h is the number of hours needed to rent the bike:
C(h) = Cost per hour * h + rental charge
Using our given numbers in the problem, we have:
C(h) = 9h + 15
The problem asks for h, when C(h) = 51.
9h + 15 = 51
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=9h%2B15%3D51&pl=Solve']plug this equation into our search engine[/URL] and we get:
h = [B]4[/B]

Of the 800 students of a school, 600 have traveled. What percentage of the students went on a trip?

Of the 800 students of a school, 600 have traveled. What percentage of the students went on a trip?
Our percentage is found as 600/800.
Simplifying by dividing top and bottom by 100, we have:
6/8
Divide top and bottom by 2, we get:
3/4 or [B]75%
[/B]
You can also type in the [URL='http://www.mathcelebrity.com/perc.php?num=600&den=800&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']search engine[/URL]: 600/800 as percent.

Of the worlds 7.5 billion people, 1.2 billion people live on less than 4 per day. Calculate the perc

Of the worlds 7.5 billion people, 1.2 billion people live on less than 4 per day. Calculate the percent of the worlds population who lives on less than 4 per day?
We want the percentage 1.2/7.5.
[URL='https://www.mathcelebrity.com/perc.php?num=1.2&den=7.5&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Type this fraction into our search engine[/URL], choose percentage, and we get:
[B]16%[/B]

On a map, every 5 cm represents 250 kilometres. What distance would be represented by a 3 cm line?

On a map, every 5 cm represents 250 kilometres. What distance would be represented by a 3 cm line?
We set up a proportion of map cm distance to kilometers where k is the kilometers represented by a 3cm line
5/250 = 3/k
To solve this proportion for k, we [URL='https://www.mathcelebrity.com/prop.php?num1=5&num2=3&den1=250&den2=k&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
k = [B]150[/B]

On a Math test, 12 students earned an A. This number is exactly 25% of the total number of students

On a Math test, 12 students earned an A. This number is exactly 25% of the total number of students in the class. How many students are in the class?
Let the total number of students be s. Since 25% is 0.25 as a decimal, We have an equation:
0.25s = 12
[URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%3D12&pl=Solve']Type this equation into our search engine[/URL], and we get:
s = [B]48[/B]

On a particular road map, 1/2 inch represents 18 miles. About how many miles apart are 2 towns that

On a particular road map, 1/2 inch represents 18 miles. About how many miles apart are 2 towns that are 2 1/2 inches apart on this map?
A) 18
B) 22 1/2
C) 36
D) 45
E) 90
Set up a proportion of inches to miles where m is the number of miles for 2 1/2 inches. Note: 1/2 = 0.5 and 2 1/2 = 2.5
0.5/18 = 2.5/m
[URL='https://www.mathcelebrity.com/prop.php?num1=0.5&num2=2.5&den1=18&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into the search engine[/URL], we get:
[B]m = 90 Answer E[/B]

On the math test, Ralph answered 17 out of 20 problems. What percent did he get right?

On the math test, Ralph answered 17 out of 20 problems. What percent did he get right?
Using our [URL='http://www.mathcelebrity.com/perc.php?num=17&den=20&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percentage calculator or entering the phrase 17 out of 20 in the search engine[/URL], we get:
[B]85%[/B]

One day a quarter of the class is absent and 21 children are present. How many children are there on

One day a quarter of the class is absent and 21 children are present. How many children are there on the class when no one is away?
If 1/4 of the class is absent, this means that 1 - 1/4 is present.
Since 1 = 4/4, we have 4/4 - 1/4 = 3/4 of the class is present.
If the full size of the class is c, then we have
3/4c = 21
[URL='https://www.mathcelebrity.com/1unk.php?num=3%2F4c%3D21&pl=Solve']Typing 3/4c = 21 into the search engine[/URL], we get:
[B]c = 28[/B]

One number exceeds another by 15. The sum of the numbers is 51. What are these numbers

One number exceeds another by 15. The sum of the numbers is 51. What are these numbers?
Let the first number be x, and the second number be y. We're given two equations:
[LIST=1]
[*]x = y + 15
[*]x + y = 51
[/LIST]
Plug (1) into (2)
(y + 15) + y = 51
Combine like terms:
2y + 15 = 51
[URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B15%3D51&pl=Solve']Plug this equation into the search engine[/URL] and we get:
[B]y = 18[/B]
Now plug this into (1) to get:
x = 18 + 15
[B]x = 33[/B]

One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a c

One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a comma to separate your answers.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]x = 1/4y
[*]x + y = 25
[/LIST]
Substitute (1) into (2)
1/4y + y = 25
Since 1/4 = 0.25, we have:
0.25y + y = 25
[URL='https://www.mathcelebrity.com/1unk.php?num=0.25y%2By%3D25&pl=Solve']Type this equation into the search engine[/URL] to get:
[B]y = 20
[/B]
Now, substitute this into (1) to solve for x:
x = 1/4y
x = 1/4(20)
[B]x = 5
[/B]
The problem asks us to separate the answers by a comma. So we write this as:
[B](x, y) = (5, 20)[/B]

One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers.

One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers.
Let the two numbers be x and y. We're given:
[LIST=1]
[*]x = 1/5y
[*]x + y = 18
[/LIST]
Substitute (1) into (2):
1/5y + y = 18
1/5 = 0.2, so we have:
1.2y = 18
[URL='https://www.mathcelebrity.com/1unk.php?num=1.2y%3D18&pl=Solve']Type 1.2y = 18 into the search engine[/URL], and we get [B]y = 15[/B].
Which means from equation (1) that:
x = 15/5
[B]x = 3
[/B]
Our final answer is [B](x, y) = (3, 15)[/B]

One number is 3 times another. Their sum is 44.

One number is 3 times another. Their sum is 44.
Let the first number be x, and the second number be y. We're given:
[LIST=1]
[*]x = 3y
[*]x + y = 44
[/LIST]
Substitute (1) into (2):
3y + y = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=3y%2By%3D44&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]y = 11[/B]
Plug this into equation (1):
x = 3(11)
[B]x = 33[/B]

one number is 3 times as large as another. Their sum is 48. Find the numbers

one number is 3 times as large as another. Their sum is 48. Find the numbers
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x = 3y
[*]x + y = 48
[/LIST]
Substitute equation (1) into equation (2):
3y + y = 48
To solve for y, [URL='https://www.mathcelebrity.com/1unk.php?num=3y%2By%3D48&pl=Solve']we type this equation into the search engine[/URL] and we get:
[B]y = 12[/B]
Now, plug y = 12 into equation (1) to solve for x:
x = 3(12)
[B]x = 36[/B]

One number is 8 times another number. The numbers are both positive and have a difference of 70.

One number is 8 times another number. The numbers are both positive and have a difference of 70.
Let the first number be x, the second number be y. We're given:
[LIST=1]
[*]x = 8y
[*]x - y = 70
[/LIST]
Substitute(1) into (2)
8y - y = 70
[URL='https://www.mathcelebrity.com/1unk.php?num=8y-y%3D70&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]y = 10[/B] <-- This is the smaller number
Plug this into Equation (1), we get:
x = 8(10)
[B]x = 80 [/B] <-- This is the larger number

One number is equal to the square of another. Find the numbers if both are positive and their sum is

One number is equal to the square of another. Find the numbers if both are positive and their sum is 650
Let the number be n. Then the square is n^2. We're given:
n^2 + n = 650
Subtract 650 from each side:
n^2 + n - 650 = 0
We have a quadratic equation. [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-650%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']We type this into our search engine[/URL] and we get:
n = 25 and n = -26
Since the equation asks for a positive solution, we use [B]n = 25[/B] as our first solution.
the second solution is 25^2 = [B]625[/B]

one number is twice a second number. the sum of those numbers is 45

one number is twice a second number. the sum of those numbers is 45.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]x = 2y
[*]x + y = 45
[/LIST]
Substitute Equation (1) into Equation (2):
2y + y = 45
[URL='https://www.mathcelebrity.com/1unk.php?num=2y%2By%3D45&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 15[/B]
Plug this into equation (1) to solve for x, and we get:
x = 2(15)
[B]x = 30[/B]

One positive number is one-fifth of another number. The difference between the two numbers is 192, f

One positive number is one-fifth of another number. The difference between the two numbers is 192, find the numbers.
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*]x = y/5
[*]x + y = 192
[/LIST]
Substitute equation 1 into equation 2:
y/5 + y = 192
Since 1 equals 5/5, we rewrite our equation like this:
y/5 = 5y/5 = 192
We have fractions with like denominators, so we add the numerators:
(1 + 5)y/5 = 192
6y/5 = 192
[URL='https://www.mathcelebrity.com/prop.php?num1=6y&num2=192&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Type this equation into our search engine[/URL], and we get:
[B]y = 160[/B]
Substitute this value into equation 1:
x = 160/5
x = [B]32[/B]

our recipe calls for 2 eggs and 3 cups of sugar. if we want to use 5 eggs, how much sugar will we ne

Our recipe calls for 2 eggs and 3 cups of sugar. if we want to use 5 eggs, how much sugar will we need?
Set up a relational proportion for eggs to cups of sugar where s is the number of cups of sugar we need for 5 eggs.
2/3 = 5/s
[URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=5&den1=3&den2=s&propsign=%3D&pl=Calculate+missing+proportion+value']Plugging this into the search engine[/URL], we get [B]7.5 cups of sugar[/B].

Out of the 485 Cookies for the bake sale, 2/5 were chocolate chip. Estimate the number of chocolate

Out of the 485 Cookies for the bake sale, 2/5 were chocolate chip. Estimate the number of chocolate chips
We want 2/5 of 485. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=485&frac2=2/5&pl=Multiply']type this in our search engine[/URL] and we get;
[B]194[/B]

Paul can walk 15 steps in 5 minutes How long does it take Paul to walk 75 steps at the same speed

Paul can walk 15 steps in 5 minutes How long does it take Paul to walk 75 steps at the same speed
Set up a proportion of steps to minutes where m is the number of minutes to walk 75 steps:
15/5 = 75/m
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=75&den1=5&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
m = [B]25[/B]

Peter has $500 in his savings account. He purchased an iPhone that charged him $75 for his activatio

Peter has $500 in his savings account. He purchased an iPhone that charged him $75 for his activation fee and $40 per month to use the service on the phone. Write an equation that models the number of months he can afford this phone.
Let m be the number of months. Our equation is:
[B]40m + 75 = 500 [/B] <-- This is the equation
[URL='https://www.mathcelebrity.com/1unk.php?num=40m%2B75%3D500&pl=Solve']Type this equation into the search engine[/URL], and we get:
m = [B]10.625[/B]
Since it's complete months, it would be 10 months.

Peter was thinking of a number. Peter doubles it and adds 0.8 to get an answer of 31. Form an equati

Peter was thinking of a number. Peter doubles it and adds 0.8 to get an answer of 31. Form an equation with x from the information.
Take this algebraic expression in parts, starting with the unknown number x:
[LIST]
[*]x
[*][I]Double it [/I]means we multiply x by 2: 2x
[*]Add 0.8: 2x + 0.8
[*]The phrase [I]to get an answer of[/I] means an equation. So we set 2x + 0.8 equal to 31
[/LIST]
Build our final algebraic expression:
[B]2x + 0.8 = 31[/B]
[B][/B]
If you have to solve for x, then we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B0.8%3D31&pl=Solve']type this equation into our search engine[/URL] and we get:
x = 15.1

Peter’s Lawn Mowing Service charges $10 per job and $0.20 per square yard. Peter earns $25 for a job

Peter’s Lawn Mowing Service charges $10 per job and $0.20 per square yard. Peter earns $25 for a job.
Let y be the number of square yards. We have the following equation:
0.2y + 10 = 25
To solve for y, we[URL='https://www.mathcelebrity.com/1unk.php?num=0.2y%2B10%3D25&pl=Solve'] type this equation into our search engine [/URL]and we get:
y = [B]75[/B]

Probability of getting 4 or 6 when rolling a dice

Probability of getting 4 or 6 when rolling a dice
P(4 or 6) = P(4) + P(6)
P(4 or 6) = 1/6 + 1/6
P(4 or 6) = 2/6
We can simplify this. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F6&frac2=3%2F8&pl=Simplify']type this fraction into our search engine, choose simplify[/URL], and we get:
P(4 or 6) = [B]1/3[/B]

q is equal to 207 subtracted from the quantity 4 times q

q is equal to 207 subtracted from the quantity 4 times q
4 time q
4q
207 subtracted from 4 times q:
4q - 207
Set this equal to q:
[B]4q - 207 = q [/B]<-- This is our algebraic expression
To solve for q, [URL='https://www.mathcelebrity.com/1unk.php?num=4q-207%3Dq&pl=Solve']type this equation into the search engine[/URL]. We get:
[B]q = 69[/B]

Rachel saved $200 and spends $25 each week. Roy just started saving $15 per week. At what week will

Rachel saved $200 and spends $25 each week. Roy just started saving $15 per week. At what week will they have the same amount?
Let Rachel's account value R(w) where w is the number of weeks be:
R(w) = 200 - 25w <-- We subtract -25w because she spends it every week, decreasing her balance.
Let Roy's account value R(w) where w is the number of weeks be:
R(w) = 15w
Set them equal to each other:
200 - 25w = 15w
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=200-25w%3D15w&pl=Solve']we type it into our search engine[/URL] and get:
[B]w = 5[/B]

Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wedne

Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she sold 6 fewer books than she did on Tuesday. During the 3 days Rachel sold 19 books. Create an equation that can be used to find m, a number of books Rachel sold on Monday.
Let me be the number of books Rachel sold on Monday. We're given Tuesday's book sales (t) and Wednesday's books sales (w) as:
[LIST=1]
[*]t = 2m
[*]w = t - 6
[*]m + t + w = 19
[/LIST]
Plug (1) and (2) into (3):
Since t = 2m and w = t - 6 --> 2m - 6, we have:
m + 2m + 2m - 6 = 19
Combine like terms:
5m - 6 = 19
[URL='https://www.mathcelebrity.com/1unk.php?num=5m-6%3D19&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]m = 5[/B]

Reece made a deposite into an account that earns 8% simple interest. After 8 years reece has earned

Reece made a deposite into an account that earns 8% simple interest. After 8 years Reece has earned 400 dollars. How much was Reece's initial deposit?
Simple interest formula:
A = P(1 + it) where P is the amount of principal to be invested, i is the interest rate, t is the time, and A is the amount accumulated with interest.
Plugging in our numbers, we get:
400 = P(1 + 0.08(8))
400 = P(1 + 0.64)
400 = 1.64P
1.64P = 400
[URL='https://www.mathcelebrity.com/1unk.php?num=1.64p%3D400&pl=Solve']Typing this problem into our search engine[/URL], we get:
P = [B]$243.90[/B]

Represent the number of inches in 7 feet

Represent the number of inches in 7 feet
We [URL='https://www.mathcelebrity.com/linearcon.php?quant=7&pl=Calculate&type=foot']type in 7 feet to our search engine and we get[/URL]:
7 feet = [B]84 inches[/B]

Researchers in Antarctica discovered a warm sea current under the glacier that is causing the glacie

Researchers in Antarctica discovered a warm sea current under the glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate if 0.06 m per day.
Which function can be used to find the thickness of the ice shelf in meters x days since the discovery?
We want to build an function I(x) where x is the number of days since the ice shelf discovery.
We start with 450 meters, and each day (x), the ice shelf loses 0.06m, which means we subtract this from 450.
[B]I(x) = 450 - 0.06x[/B]

Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages

Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages.
Let r be Richard's age. And a be Alvin's age. We have:
[LIST=1]
[*]r = 3a
[*]a + r = 52
[/LIST]
Substitute (1) into (2)
a + 3a = 52
Group like terms:
4a = 52
[URL='https://www.mathcelebrity.com/1unk.php?num=4a%3D52&pl=Solve']Typing this into the search engine[/URL], we get [B]a = 13[/B].
This means Richard is 3(13) = [B]39[/B]

Ricky reads 20 pages in 50 minutes. How many minutes does it take him to read one page

Ricky reads 20 pages in 50 minutes. How many minutes does it take him to read one page
Set up a proportion of pages per minute where m is the number of minutes to read one page:
20/50 = 1/m
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=20&num2=1&den1=50&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
m = [B]2.5[/B]

Rico was born 6 years after Nico. The sum of their age is 36. How old is Nico?

Rico was born 6 years after Nico. The sum of their age is 36. How old is Nico?
Let Rico's age be r
Let Nico's age be n
We're given two equations:
[LIST=1]
[*]r = n + 6
[*]n + r = 36
[/LIST]
We plug equation (1) into equation (2) for r:
n + n + 6 = 36
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2Bn%2B6%3D36&pl=Solve']type it in our search engine[/URL] and we get:
[B]n = 15[/B]

Rigby and Eleanor's combined score on the systems of equations test was 181. Rigby scored 9 more poi

Rigby and Eleanor's combined score on the systems of equations test was 181. Rigby scored 9 more points than Eleanor. What were Eleanor and Rigby's scores?
Let Rigby's score be r
Let Eleanor's score be e
We're given two equations:
[LIST=1]
[*]r = e + 9
[*]e + r = 181
[/LIST]
Substitute equation (1) into equation (2):
e + (e + 9) = 181
Group like terms:
2e + 9 = 181
To solve this equation for e, we [URL='https://www.mathcelebrity.com/1unk.php?num=2e%2B9%3D181&pl=Solve']type it in our search engine[/URL] and we get:
e = [B]86[/B]

Riley is trying to raise money by selling key chains. each key chain costs $2.50. If riley is trying

Riley is trying to raise money by selling key chains. each key chain costs $2.50. If riley is trying to raise $60. How many key chains will he have to sell
Let the number of key chains be k. We have the following equation:
2.50k = 60
To solve this equation for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.50k%3D60&pl=Solve']type it in our search engine[/URL] and we get:
k = [B]24[/B]

Rose weighs 140 pounds and gains 10%. What percent of her new weight must she lose to get back to 14

Rose weighs 140 pounds and gains 10%. What percent of her new weight must she lose to get back to 140 pounds?
Find her new weight after the 10% gain:
New Weight = Starting Weight * (1 + 10%)
Since 10% is 0.1, we have:
New Weight = Starting Weight * (1 + 0.1)
New Weight = Starting Weight * (1.1)
Plug in our numbers:
New Weight = 140 * (1.1)
New Weight = 154
To get back to 140, Rose must lose 154 - 140 = 14 pounds.
As a percentage of her new weight, [URL='https://www.mathcelebrity.com/perc.php?num=14&den=154&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']we type 14/154 into our search engine[/URL], and get:
[B]9.09%
[/B]
[I]We read this as, Rose must lose 9.09% of her current body weight of 154 pounds to get back to her starting weight of 140 pounds.[/I]

Sadie and Connor both play soccer. Connor scored 2 times as many goals as Sadie. Together they score

Sadie and Connor both play soccer. Connor scored 2 times as many goals as Sadie. Together they scored 9 goals. Could Sadie have scored 4 goals? Why or why not?
[U]Assumptions:[/U]
[LIST]
[*]Let Connor's goals be c
[*]Let Sadie's goals be s
[/LIST]
We're given the following simultaneous equations:
[LIST=1]
[*]c = 2s
[*]c + s = 9
[/LIST]
We substitute equation (1) into equation (2) for c:
2s + s = 9
To solve the equation for s, we type it in our search equation and we get:
s = [B]3[/B]
So [U][B]no[/B][/U], Sadie could not have scored 4 goals since s = 3

sales 45,000 commission rate is 3.6% and salary is $275

sales 45,000 commission rate is 3.6% and salary is $275
Set up the commission function C(s) where s is the salary:
C(s) = Commission * s + salary
We're given: C(s) = 45,000, commission = 3.6%, which is 0.036 and salary = 275, so we have:
0.036s + 275 = 45000
To solve for s, we type this equation into our search engine and we get:
s = [B]1,242,361.11[/B]

Sales tax is directly proportional to cost. If the sales tax on a 46000 automobile is $240, what is

Sales tax is directly proportional to cost. If the sales tax on a 46000 automobile is $240, what is the sales tax on a $9000 automobile?
Set up a proportion of sales tax to purchase price where s is the sales tax on a 9000 automobile:
240/46000 = s/9000
[URL='https://www.mathcelebrity.com/prop.php?num1=240&num2=s&den1=46000&den2=9000&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL] and we get:
s = [B]46.96[/B]

Sally and Adam works a different job. Sally makes $5 per hour and Adam makes $4 per hour. They each

Sally and Adam works a different job. Sally makes $5 per hour and Adam makes $4 per hour. They each earn the same amount per week but Adam works 2 more hours. How many hours a week does Adam work?
[LIST]
[*]Let [I]s[/I] be the number of hours Sally works every week.
[*]Let [I]a[/I] be the number of hours Adam works every week.
[*]We are given: a = s + 2
[/LIST]
Sally's weekly earnings: 5s
Adam's weekly earnings: 4a
Since they both earn the same amount each week, we set Sally's earnings equal to Adam's earnings:
5s = 4a
But remember, we're given a = s + 2, so we substitute this into Adam's earnings:
5s = 4(s + 2)
Multiply through on the right side:
5s = 4s + 8 <-- [URL='https://www.mathcelebrity.com/expand.php?term1=4%28s%2B2%29&pl=Expand']multiplying 4(s + 2)[/URL]
[URL='https://www.mathcelebrity.com/1unk.php?num=5s%3D4s%2B8&pl=Solve']Typing this equation into the search engine[/URL], we get s = 8.
The problem asks for Adam's earnings (a). We plug s = 8 into Adam's weekly hours:
a = s + 2
a = 8 + 2
[B]a = 10[/B]

Sally found 73 seashells on the beach, she gave Mary some of her seashells. She has 10 left. How man

Sally found 73 seashells on the beach, she gave Mary some of her seashells. She has 10 left. How many did she give to Mary?
Let the number of seashells Sally gave away as g. We're given:
73 - g = 10
To solve this equation for g, we [URL='https://www.mathcelebrity.com/1unk.php?num=73-g%3D10&pl=Solve']type it in our search engine[/URL] and we get:
g = [B]63[/B]

Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64.

Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64.
Let Sally's age be s. Let Mark's age be m. We're given two equations:
[LIST=1]
[*]s = m + 4
[*]2s + 5m = 64 <-- [I]Since Twice means we multiply by 2[/I]
[/LIST]
Substitute equation (1) into equation (2):
2(m + 4) + 5m = 64
Multiply through:
2m + 8 + 5m = 64
Group like terms:
(2 + 5)m + 8 = 64
7m + 8 = 64
[URL='https://www.mathcelebrity.com/1unk.php?num=7m%2B8%3D64&pl=Solve']Type this equation into the search engine[/URL] and we get:
m = [B]8[/B]

Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which

Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy's age, j, if he is the younger man.
Let Sam's age be s. Let' Jeremy's age be j. We're given:
[LIST=1]
[*]s = j + 2 <-- consecutive odd integers
[*]sj = 783
[/LIST]
Substitute (1) into (2):
(j + 2)j = 783
j^2 + 2j = 783
Subtract 783 from each side:
j^2 + 2j - 783 = 0 <-- This is the equation to find Jeremy's age.
To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=j%5E2%2B2j-783%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this quadratic equation into the search engine[/URL] and get:
j = 27, j = -29.
Since ages cannot be negative, we have:
[B]j = 27[/B]

Sam bought 8 new basketball trading cards to add to his collection. The next day his dog ate half of

Sam bought 8 new basketball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 40 cards left. How many cards did Sam start with?
Let the starting about of cards be s.
Sam adds 8 new cards, so he has s + 8.
Then the dog ate half, so he's left with half. Sam is left with 40 cards:
(s + 8)/2 = 40
Cross multiply:
s + 8 = 80
[URL='https://www.mathcelebrity.com/1unk.php?num=s%2B8%3D80&pl=Solve']Type s + 8 = 80 into the search engine[/URL], and we get [B]s = 72[/B]

Sam can pick 56 apples in 30 minutes. How many can he pick in 45 minutes?

Sam can pick 56 apples in 30 minutes. How many can he pick in 45 minutes?
We set up a proportion of apples to minutes where a is the number of apples Sam can pick in 45 minutes.
56/30 = a/45
Using our math engine, we [URL='https://www.mathcelebrity.com/prop.php?num1=56&num2=a&den1=30&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search box[/URL] and get:
a = [B]84
[MEDIA=youtube]tpNHh1jh3XE[/MEDIA][/B]

Sam finished 18 problems in one hour. How many hours will it take same to solve 80 problems

Sam finished 18 problems in one hour. How many hours will it take same to solve 80 problems
Set up a proportion of problems to hours where h is the number of hours for 80 problems:
18/1 = 80/h
To solve for h, we [URL='https://www.mathcelebrity.com/prop.php?num1=18&num2=80&den1=1&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search engine [/URL]and we get:
h = [B]4.44[/B]

Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John

Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John
Let John's age be j. We're given the following equation:
3j - 20 = 52 ([I]Less than[/I] means we subtract)
To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=3j-20%3D52&pl=Solve']type this equation into our search engine[/URL] and we get:
j = [B]24[/B]

Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money fro

Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money from her account and still have money left?
Let w be the number of weeks. We have the following equation for the Balance after w weeks:
B(w) = 250 - 25w [I]we subtract for withdrawals[/I]
The ability to withdrawal money means have a positive or zero balance after withdrawal. So we set up the inequality below:
250 - 25w >= 0
To solve this inequality for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=250-25w%3E%3D0&pl=Solve']type it in our search engine[/URL] and we get:
w <= [B]10
So Sarah can withdrawal for up to 10 weeks[/B]

Sarah makes $9 per hour working at a daycare center and $12 per hour working at a restaurant. Next

Sarah makes $9 per hour working at a daycare center and $12 per hour working at a restaurant. Next week, Sarah is scheduled to work 8 hours at the daycare center. Which of the following inequalities represents the number of hours (h) that Sandra needs to work at the restaurant next week to earn at least $156 from these two jobs?
Set up Sarah's earnings function E(h) where h is the hours Sarah must work at the restaurant:
12h + 9(8) >= 156 <-- The phrase [I]at least[/I] means greater than or equal to, so we set this up as an inequality. Also, the daycare earnings are $9 per hour * 8 hours
Multiplying through and simplifying, we get:
12h + 72 >= 156
We [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B72%3E%3D156&pl=Solve']type this inequality into the search engine[/URL], and we get:
[B]h>=7[/B]

Sarah splits her 87 Pokémon cards into 9 piles. How many are left over?

Sarah splits her 87 Pokémon cards into 9 piles. How many are left over?
We want the reminder of 87/9, so we t[URL='https://www.mathcelebrity.com/modulus.php?num=87mod9&pl=Calculate+Modulus']ype 87 mod 9 into our search engine and we get[/URL]:
87 mod 9 =[B] 6[/B]

Select 6 bills from a combination of 5 different bills

We use the combination formula, 6 choose 5, or 6C5.
Using our [URL='http://www.mathcelebrity.com/permutation.php?num=6&den=5&pl=Combinations']combinations calculator[/URL], or entering 6C6 into the search engine, we get
[B]6 ways to select.[/B]

set of all continents

set of all continents
Our set of 7 elements is below:
{[B]Africa, Antarctica, Asia, Australia/Oceania, Europe, North America, and South America[/B].}

Shanice won 97 pieces of gum playing basketball at the county fair. At school she gave four to every

Shanice won 97 pieces of gum playing basketball at the county fair. At school she gave four to every student in her math class. She only has 5 remaining. How many students are in her class?
Let the number of students be s. We have a situation described by the following equation:
4s + 5 = 97 <-- We add 5 since it's left over to get to 97
[URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B5%3D97&pl=Solve']We type this equation into the search engine[/URL] and we get:
s = [B]23[/B]

She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked bot

She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked both jobs for a total of 30 hours, and a total of $690. How long did Giselle work as a carpenter and how long did she work as a blacksmith?
Assumptions:
[LIST]
[*]Let b be the number of hours Giselle worked as a blacksmith
[*]Let c be the number of hours Giselle worked as a carpenter
[/LIST]
Givens:
[LIST=1]
[*]b + c = 30
[*]25b + 20c = 690
[/LIST]
Rearrange equation (1) to solve for b by subtracting c from each side:
[LIST=1]
[*]b = 30 - c
[*]25b + 20c = 690
[/LIST]
Substitute equation (1) into equation (2) for b
25(30 - c) + 20c = 690
Multiply through:
750 - 25c + 20c = 690
To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=750-25c%2B20c%3D690&pl=Solve']type this equation into our search engine[/URL] and we get:
c = [B]12
[/B]
Now, we plug in c = 12 into modified equation (1) to solve for b:
b = 30 - 12
b = [B]18[/B]

Sheila loaded 21 trucks every 28 minutes. At this rate how long will it take to load 12 trucks

Sheila loaded 21 trucks every 28 minutes. At this rate how long will it take to load 12 trucks.
Let m be the number of minutes it takes Sheila to load 12 trucks. We set up a proportion of trucks to minutes:
21/28 = 12/m
[URL='https://www.mathcelebrity.com/prop.php?num1=21&num2=12&den1=28&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL],and we get:
m = [B]16[/B]

Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry?

Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry?
Let Sherry's age be s. Let the mom's age be m. We're given two equations:
[LIST=1]
[*]s = m - 31
[*]m + s = 61
[/LIST]
Substitute equation (1) into equation (2) for s:
m + m - 31 = 61
To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm-31%3D61&pl=Solve']we type this equation into our search engine[/URL] and we get:
m = 46
Now, we plug m = 46 into equation (1) to find Sherry's age s:
s = 46 - 31
s = [B]15[/B]

show how 6 people could share 4 sandwiches.

show how 6 people could share 4 sandwiches.
[URL='https://www.mathcelebrity.com/search.php?q=4%2F6&x=0&y=0']4/6 = [/URL]2/3
Cut each of the 4 sandwiches in 3 pieces.
this gives us 4 * 3 = 12
[B]Each person gets 2[/B] of the 12 slices because 12 * 2/3 = 6

Sierra borrows $310 from her brother to buy a lawn mower. She will repay $85 to start, and then anot

Sierra borrows $310 from her brother to buy a lawn mower. She will repay $85 to start, and then another $25 per week. A. Write an equation that can be used to determine w, the number of weeks it will take for Sierra to repay the entire amount.
Let w be the number of weeks. We have the equation:
25w + 85 = 310
[URL='https://www.mathcelebrity.com/1unk.php?num=25w%2B85%3D310&pl=Solve']Type this equation into the search engine[/URL], and we get:
w = [B]9[/B]

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 c

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point.
Calculate the revenue function R(c) where s is the number of sodas sold:
R(s) = Sale Price * number of units sold
R(s) = 50s
Calculate the cost function C(s) where s is the number of sodas sold:
C(s) = Variable Cost * s + Fixed Cost
C(s) = 0.25s + 900
Our break-even point is found by setting R(s) = C(s):
0.25s + 900 = 50s
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B900%3D50s&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]18.09[/B]

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Stacy and Travis are rock climbing. Stacys rope is 4 feet shorter than 3 times the length of Travis

Stacy and Travis are rock climbing. Stacys rope is 4 feet shorter than 3 times the length of Travis rope. Stacys rope is 23 feet long. Write and solve an equation to find the length t of Travis rope.
Let Stacy's rope be s. Travis's rope be t. We have:
s = 3t - 4
s = 23
So [B]3t - 4 = 23
[/B]
[URL='http://www.mathcelebrity.com/1unk.php?num=3t-4%3D23&pl=Solve']Paste this equation into our search engine[/URL] to get [B]t = 9[/B].

Steven has some money. If he spends $9, then he will have 3/5 of the amount he started with.

Steven has some money. If he spends $9, then he will have 3/5 of the amount he started with.
Let the amount Steven started with be s. We're given:
s - 9 = 3s/5
Multiply each side through by 5 to eliminate the fraction:
5(s - 9) = 5(3s/5)
Cancel the 5's on the right side and we get:
5s - 45 = 3s
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=5s-45%3D3s&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]22.5[/B]

sum of a number and 7 is subtracted from 15 the result is 6.

Sum of a number and 7 is subtracted from 15 the result is 6.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take this expression in pieces. Sum of a number and 7
x + 7
Subtracted from 15
15 - (x + 7)
The result is means an equation, so we set this expression above equal to 6
[B]15 - (x + 7) = 6 <-- This is our algebraic expression[/B]
If the problem asks you to solve for x, we Group like terms
15 - x - 7 = 6
8 - x = 6
[URL='https://www.mathcelebrity.com/1unk.php?num=8-x%3D6&pl=Solve']Type 8 - x = 6 into the search engine[/URL], and we get [B]x = 2[/B]

Sum of a number and it's reciprocal is 6. What is the number?

Sum of a number and it's reciprocal is 6. What is the number?
Let the number be n.
The reciprocal is 1/n.
The word [I]is[/I] means an equation, so we set n + 1/n equal to 6
n + 1/n = 6
Multiply each side by n to remove the fraction:
n^2 + 1 = 6n
Subtract 6n from each side:
[B]n^2 - 6n + 1 = 0 [/B]<-- This is our algebraic expression
If the problem asks you to solve for n, then you [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-6n%2B1%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type this quadratic equation into our search engine[/URL].

Sum of N and its next consecutive even integer is 65

Sum of N and its next consecutive even integer is 65
Next even consecutive integer is N + 2.
We have N + (N + 2) = 65.
Combine like terms, we have 2N + 2 = 65
[URL='http://www.mathcelebrity.com/1unk.php?num=2n%2B2%3D65&pl=Solve']Running this problem through the search engine[/URL], we get n = 31.5. Meaning this problem is impossible, it cannot be done. n is not an integer, and neither is the next consecutive even integer.

SuperFit Gym charges $14 per month, as well as a one-time membership fee of $25 to join. After how m

SuperFit Gym charges $14 per month, as well as a one-time membership fee of $25 to join. After how many months will I spend a total of $165?
[U]Let the number of months be m. We have a total spend T of:[/U]
cost per month * m + one-time membership fee = T
[U]Plugging in our numbers, we get:[/U]
14m + 25 = 165
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=14m%2B25%3D165&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]10[/B]

Suppose that 17 inches of wire costs 51 cents at the same rate, how many inches of wire can be bough

Suppose that 17 inches of wire costs 51 cents at the same rate, how many inches of wire can be bought for 42 cents?
Set up a proportion of inches of wire to cost, were w equals the inches of wire at 42 cents. We have:
17/51 = w/42
[URL='https://www.mathcelebrity.com/prop.php?num1=17&num2=w&den1=51&den2=42&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], we get:
[B]w = 14[/B]

Suppose that h(x) varies directly with x and h(x)=44 when x = 2. What is h(x) when x = 1.5?

Suppose that h(x) varies directly with x and h(x)=44 when x = 2. What is h(x) when x = 1.5?
Direct variation means we set up an equation:
h(x) = kx where k is the constant of variation.
For h(x) = 44 when x = 2, we have:
2k = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=2k%3D44&pl=Solve']Type this equation into our search engine[/URL], we get:
k = 22
The question asks for h(x) when x = 1.5. So we set up our variation equation, knowing that k = 22.
kx = h(x)
With k = 22 and x = 1.5, we get:
22(1.5) = h(x)
h(x) = [B]33[/B]

Suppose we need 4 eggs to make a cake. If there are 24 eggs, write an inequality representing the po

Suppose we need 4 eggs to make a cake. If there are 24 eggs, write an inequality representing the possible number of cakes we can make.
Set up a proportion of eggs to cakes where c is the number of cakes per 24 eggs:
4/1 <= 24/c
[URL='https://www.mathcelebrity.com/prop.php?num1=4&num2=24&den1=1&den2=c&propsign=%3C&pl=Calculate+missing+proportion+value']Typing this proportion inequality into our search engine[/URL], we get:
[B]c <= 6[/B]

Suppose you are asked to choose three movies. If there are 20 different movies, in how many ways can

Suppose you are asked to choose three movies. If there are 20 different movies, in how many ways can the three movies be chosen?
We want unique combinations, so we have 20 choose 3:
We [URL='https://www.mathcelebrity.com/permutation.php?num=20&den=3&pl=Combinations']type 20C3 into our search engine[/URL] and we get:
20C3 = [B]1,140[/B]

Suppose you have $28.00 in your bank account and start saving $18.25 every week. Your friend has $16

Suppose you have $28.00 in your bank account and start saving $18.25 every week. Your friend has $161.00 in his account and is withdrawing $15 every week. When will your account balances be the same?
Set up savings and withdrawal equations where w is the number of weeks. B(w) is the current balance
[LIST]
[*]You --> B(w) = 18.25w + 28
[*]Your friend --> B(w) = 161 - 15w
[/LIST]
Set them equal to each other
18.25w + 28 = 161 - 15w
[URL='http://www.mathcelebrity.com/1unk.php?num=18.25w%2B28%3D161-15w&pl=Solve']Type that problem into the search engine[/URL], and you get [B]w = 4[/B].

Suppose you write a book. The printer charges $4 per book to print it, and you spend 5500 on adverti

Suppose you write a book. The printer charges $4 per book to print it, and you spend 5500 on advertising. You sell the book for $15 a copy. How many copies must you sell to break even.
Profit per book is:
P = 15 - 4
P = 11
We want to know the number of books (b) such that:
11b = 5500 <-- Breakeven means cost equals revenue
[URL='https://www.mathcelebrity.com/1unk.php?num=11b%3D5500&pl=Solve']Typing this equation into the search engine[/URL], we get:
b = [B]500[/B]

Susan makes and sells purses. The purses cost her $15 each to make, and she sells them for $30 each.

Susan makes and sells purses. The purses cost her $15 each to make, and she sells them for $30 each. This Saturday, she is renting a booth at a craft fair for $50. Write an equation that can be used to find the number of purses Susan must sell to make a profit of $295
Set up the cost function C(p) where p is the number of purses:
C(p) = Cost per purse * p + Booth Rental
C(p) = 15p + 50
Set up the revenue function R(p) where p is the number of purses:
R(p) = Sale price * p
R(p) = 30p
Set up the profit function which is R(p) - C(p) equal to 295
30p - (15p + 50) = 295
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=30p-%2815p%2B50%29%3D295&pl=Solve']we type it into our search engine[/URL] and we get:
p = [B]23[/B]

Tamara can proofread 16 pages in 8 minutes. How many minutes will it take her to proofread 108 pages

Tamara can proofread 16 pages in 8 minutes. How many minutes will it take her to proofread 108 pages
Set up a proportion of pages to minutes:
16 pages/8 minutes = 108 pages / p minutes
We want to solve for p.
Type [I][URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=108&den1=8&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']16/8 = 108/p[/URL][/I] into the search engine.
We get p = [B]54 minutes[/B]

Tamira and her 3 friends spent a total of $37 for a large pizza and 4 sodas. Each soda cost $2. Whic

Tamira and her 3 friends spent a total of $37 for a large pizza and 4 sodas. Each soda cost $2. Which equation can be used to find p, the cost of the pizza?
We add the cost of the pizza (p) to the 4 sodas @ $2 each to get 37
p + 4(2) = 37
[B]p + 8 = 37 (This is the equation)
[/B]
If the problem asks you to solve for p, then we [URL='https://www.mathcelebrity.com/1unk.php?num=p%2B8%3D37&pl=Solve']type the equation above into our search engine[/URL] and we get:
p = [B]29[/B]

The age of three sister are consecutive intergers the sum of their age is 45 what is their ages

The age of three sister are consecutive intergers the sum of their age is 45 what is their ages
Type this into the search engine: [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=thesumofthreeconsecutivenumbersis45&pl=Calculate']The sum of three consecutive numbers is 45[/URL].
We get [B]14, 15, 16[/B].

The ages of three siblings are all consecutive integers. The sum of of their ages is 39.

The ages of three siblings are all consecutive integers. The sum of of their ages is 39.
Let the age of the youngest sibling be n. This means the second sibling is n + 1. This means the oldest/third sibling is n + 2.
So what we want is the[URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof3consecutiveintegersequalto39&pl=Calculate'] sum of 3 consecutive integers equal to 39[/URL]. We type this command into our search engine. We get:
n = 12. So the youngest sibling is [B]12[/B].
The next sibling is 12 + 1 = [B]13[/B]
The oldest/third sibling is 12 + 2 = [B]14[/B]

The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. Wha

The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. What is the value of N ?
Average of the first number set is [URL='https://www.mathcelebrity.com/statbasic.php?num1=17%2C26%2C42%2C59&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']using our average calculator[/URL] is:
36
Now, the mean (average) or 19 and N is found by adding them together an dividing by 2:
(19 + N)/2
Since both number sets have equal means, we set (19 + N)/2 equal to 36:
(19 + N)/2 = 36
Cross multiply:
19 + N = 36 * 2
19 + n = 72
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=19%2Bn%3D72&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]53[/B]

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height re

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height remained the same. What is the height of the mother?
[LIST]
[*]Let the height of the family without the mom be f. Let the height of the mother be m.
[*]Averages mean we add the heights and divide by the number of people who were measured.
[/LIST]
We're given two equations:
[LIST=1]
[*](f + m)/6 = 6
[*]f/5 = 6
[/LIST]
Cross multiplying equation (2), we get:
f = 5 * 6
f = 30
Plug f = 30 into equation (1), we get:
(30 + m)/6 = 6
Cross multiplying, we get:
m + 30 = 6 * 6
m + 30 = 36
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B30%3D36&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]6[/B]
[SIZE=3][FONT=Arial][COLOR=rgb(34, 34, 34)][/COLOR][/FONT][/SIZE]

The average of 16 and x is 21. Find x.

The average of 16 and x is 21. Find x.
The average of 2 numbers is the sum of the 2 numbers divided by 2. So we have:
(16 + x)/2 = 21
Cross multiply:
16 + x = 21*2
16 + x = 42
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2Bx%3D42&pl=Solve']we type this expression into the search engine[/URL] and get [B]x = 26[/B].
Check our work by restating our answer:
The average of 16 and 26 is 21. TRUE.

The bigger of 2 numbers in 5 larger than the smaller. Twice the smaller, increased by, twice the lar

The bigger of 2 numbers in 5 larger than the smaller. Twice the smaller, increased by, twice the larger, is equal to 50. Find each number.
Let the big number be b. Let the small number be s. We're given two equations:
[LIST=1]
[*]b = s + 5
[*]2s + 2b = 50
[/LIST]
Substitute equation (1) into equation (2)
2s + 2(s + 5) = 50
[URL='https://www.mathcelebrity.com/1unk.php?num=2s%2B2%28s%2B5%29%3D50&pl=Solve']Type this equation into our search engine[/URL], and we get:
[B]s = 10[/B]
Now substitute s = 10 into equation (1) to solve for b:
b = 10 + 5
[B]b = 15[/B]

The bill for the repair of a car was $294. The cost of parts was $129, and labor charge was $15 per

The bill for the repair of a car was $294. The cost of parts was $129, and labor charge was $15 per hour. How many hours did it take to repair the car? Write a sentence as your answer.
Let h be the number of hours. We have:
15h + 129 = 294
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=15h%2B129%3D294&pl=Solve']type it in the search engine [/URL]and we get:
h = [B]11[/B]

The bill from your plumber was $134. The cost for labor was $32 per hour. The cost materials was $46

The bill from your plumber was $134. The cost for labor was $32 per hour. The cost materials was $46. How many hours did the plumber work?
Set up the cost equation where h is the number of hours worked:
32h + 46 = 134
[URL='https://www.mathcelebrity.com/1unk.php?num=32h%2B46%3D134&pl=Solve']Typing this equation into our search engine[/URL], we get [B]h = 2.75[/B].

The Canucks lost 6 of their first 24 games. At this rate how many would the lose in an 84 game sched

The Canucks lost 6 of their first 24 games. At this rate how many would the lose in an 84 game schedule?
Set up a proportion of losses to games where l is the number of losses for 84 games:
6/24 = l/84
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=l&den1=24&den2=84&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
l = [B]21[/B]

The circle has an arc measure of 180 degrees

The circle has an arc measure of 180 degrees - True or False.
False. A Circle has an arc measure of 360 degrees.
A few vital facts about arcs measures, also called central angles:
[LIST=1]
[*]An arc measure [I]< [/I]180° is a minor arc.
[*]An arc measure [I]> [/I]180° is a major arc.
[*]An arc measure [I]= [/I]180° is a semicircle.
[*]An arc measure [I]= 36[/I]0° is a circle.
[/LIST]

The coach writes the batting order on a piece of paper. How many different ways could the list be wr

The coach writes the batting order on a piece of paper. How many different ways could the list be written?
We have 9 people in a line up. The total lineups are shown by:
9 * 8 * 7 * ... * 2 * 1
Or, 9!. [URL='https://www.mathcelebrity.com/factorial.php?num=9!&pl=Calculate+factorial']Typing 9! in our search engine[/URL] and we get [B]362,880[/B]

The cost of 25 apples is less than $9.50. The cost of 12 apples is more than 3.60. What are the poss

The cost of 25 apples is less than $9.50. The cost of 12 apples is more than 3.60. What are the possible prices of one apple?
Let a be the price of each apple. We're given 2 inequalities:
[LIST=1]
[*]25a < 9.50
[*]12a > 3.60
[/LIST]
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=25a%3C9.50&pl=Show+Interval+Notation']Typing 25a < 9.50 into our search engine[/URL], we get a < 0.38
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=12a%3E3.60&pl=Show+Interval+Notation']Typing 12a > 360 into our search engine[/URL], we get a > 0.3
Therefore, the possible prices a of one apple are expressed as the inequality:
[B]0.3 < a < 0.38[/B]

The cost of a gallon of milk (m) is .50 more than 5 times the cost of a gallon of water (w). If a ga

The cost of a gallon of milk (m) is .50 more than 5 times the cost of a gallon of water (w). If a gallon of milk cost 3.75, what is the cost of a gallon of water?
We're given:
m = 5w + 0.50
m = $3.75
Set them equal to each other:
5w + 0.50 = 3.75
[URL='https://www.mathcelebrity.com/1unk.php?num=5w%2B0.50%3D3.75&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 0.65[/B]

The dance committee of pine bluff middle school earns $72 from a bake sale and will earn $4 for each

The dance committee of pine bluff middle school earns $72 from a bake sale and will earn $4 for each ticket sold they sell to the Spring Fling dance. The dance will cost $400
Let t be the number of tickets sold. We have a Revenue function R(t):
R(t) = 4t + 72
We want to know t such that R(t) = 400. So we set R(t) = 400:
4t + 72 = 400
[URL='https://www.mathcelebrity.com/1unk.php?num=4t%2B72%3D400&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]t = 82[/B]

The denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 is

The denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 is added to the denominator, the value of the fraction is 1/2. Find the original fraction.
Let the original fraction be n/d.
We're given:
[LIST=1]
[*]d = n + 4
[*](n + 4) / (d + 7) = 1/2
[/LIST]
Cross multiply Equation 2:
2(n + 4) = d + 7
2n + 8 = d + 7
Now substitute equation (1) into tihs:
2n + 8 = (n + 4) + 7
2n + 8 = n + 11
[URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B8%3Dn%2B11&pl=Solve']Type this equation into our search engine[/URL], and we get:
n = 3
This means from equation (1), that:
d = 3 + 4
d = 7
So our original fraction n/d = [B]3/7[/B]

The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. Wh?

The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. What are the numbers?
Let the smaller number be x. Let the larger number be y. We're given:
[LIST=1]
[*]y - x = 108
[*]6x = y + 2
[/LIST]
Rearrange (1) by adding x to each side:
[LIST=1]
[*]y = x + 108
[/LIST]
Substitute this into (2):
6x = x + 108 + 2
Combine like terms
6x = x +110
Subtract x from each side:
5x = 110
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D110&pl=Solve']Plugging this equation into our search engine[/URL], we get:
x = [B]22[/B]

The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is

The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number
Let the smaller number be s. Let the larger number be l. We're given two equations:
[LIST=1]
[*]l - s = 25
[*]s = l/6
[/LIST]
Plug in equation (2) into equation (1):
l - l/6 = 25
Multiply each side of the equation by 6 to remove the fraction:
6l - l = 150
To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=6l-l%3D150&pl=Solve']type this equation into our search engine[/URL] and we get:
l = 30
To solve for s, we plug in l = 30 into equation (2) above:
s = 30/6
[B]s = 5[/B]

The difference between two positive numbers is 5 and the square of their sum is 169

The difference between two positive numbers is 5 and the square of their sum is 169.
Let the two positive numbers be a and b. We have the following equations:
[LIST=1]
[*]a - b = 5
[*](a + b)^2 = 169
[*]Rearrange (1) by adding b to each side. We have a = b + 5
[/LIST]
Now substitute (3) into (2):
(b + 5 + b)^2 = 169
(2b + 5)^2 = 169
[URL='https://www.mathcelebrity.com/community/forums/calculator-requests.7/create-thread']Run (2b + 5)^2 through our search engine[/URL], and you get:
4b^2 + 20b + 25
Set this equal to 169 above:
4b^2 + 20b + 25 = 169
[URL='https://www.mathcelebrity.com/quadratic.php?num=4b%5E2%2B20b%2B25%3D169&pl=Solve+Quadratic+Equation&hintnum=+0']Run that quadratic equation in our search engine[/URL], and you get:
b = (-9, 4)
But the problem asks for [I]positive[/I] numbers. So [B]b = 4[/B] is one of our solutions.
Substitute b = 4 into equation (1) above, and we get:
a - [I]b[/I] = 5
[URL='https://www.mathcelebrity.com/1unk.php?num=a-4%3D5&pl=Solve']a - 4 = 5[/URL]
[B]a = 9
[/B]
Therefore, we have [B](a, b) = (9, 4)[/B]

The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown n

The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown number.
The phrase a number uses the variable w.
3 times w is written as 3w
The difference of 3w and 6 is written as 3w - 6
Set this equal to 7
[B]3w - 6 = 7
[/B]
This is our algebraic expression. To solve this equation for w, we [URL='http://www.mathcelebrity.com/1unk.php?num=3w-6%3D7&pl=Solve']type the algebraic expression into our search engine[/URL].

The difference of twice a number and 4 is at least -27

The difference of twice a number and 4 is at least -27.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Twice a number means multiply the number by 2
2x
[I]and 4[/I] means we add 4 to our expression:
2x + 4
[I]Is at least[/I] means an inequality. In this case, it's greater than or equal to:
[B]2x + 4 >= -27
[/B]
To solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B4%3E%3D-27&pl=Solve']type it in the search engine[/URL].

the difference of twice a number and 8 is at most -30

the difference of twice a number and 8 is at most -30.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Twice this number means we multiply by 2, so we have 2x.
We take the difference of 2x and 8, meaning we subtract 8:
2x - 8
Finally, the phrase [I]at most[/I] means an inequality, also known as less than or equal to:
[B]2x - 8 <= 30 <-- This is our algebraic expression
[/B]
To solve this, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x-8%3C%3D30&pl=Solve']type it into the search engine[/URL] and get x <= 19.

The difference of two numbers is 12 and their mean is 15. Find the two numbers

The difference of two numbers is 12 and their mean is 15. Find the two numbers.
Let the two numbers be x and y. We're given:
[LIST=1]
[*]x - y = 12
[*](x + y)/2 = 15. <-- Mean is an average
[/LIST]
Rearrange equation 1 by adding y to each side:
x - y + y = y + 12
Cancelling the y's on the left side, we get:
x = y + 12
Now substitute this into equation 2:
(y + 12 + y)/2 = 15
Cross multiply:
y + 12 + y = 30
Group like terms for y:
2y + 12 = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B12%3D30&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 9[/B]
Now substitute this into modified equation 1:
x = y + 12
x = 9 + 12
[B]x = 21[/B]

The difference of two numbers is 720. The smaller of the numbers is 119. What is the other number?

The difference of two numbers is 720. The smaller of the numbers is 119. What is the other number?
Let the larger number be l. We're given:
l - 119 = 720
[URL='https://www.mathcelebrity.com/1unk.php?num=l-119%3D720&pl=Solve']We type this equation into the search engine[/URL] and we get:
l = [B]839[/B]

The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased by x cm and its width i

The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased
by x cm and its width is increased by x cm, its area is increased by 35 sq. cm.
a. Express the new length and the new width in terms of x.
b. Express the new area of the rectangle in terms of x.
c. Find the value of x.
Calculate the current area. Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=30&w=18&a=&p=&pl=Calculate+Rectangle']rectangle calculator with length = 30 and width = 18[/URL], we get:
A = 540
a) Decrease length by x and increase width by x, and we get:
[LIST]
[*]length = [B]30 - x[/B]
[*]width = [B]18 + x[/B]
[/LIST]
b) Our new area using the lw = A formula is:
(30 - x)(18 + x) = 540 + 35
Multiplying through and simplifying, we get:
540 - 18x + 30x - x^2 = 575
[B]-x^2 + 12x + 540 = 575[/B]
c) We have a quadratic equation. To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=-x%5E2%2B12x%2B540%3D575&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine, choose solve[/URL], and we get:
[B]x = 5 or x = 7[/B]
Trying x = 5, we get:
A = (30 - 5)(18 + 5)
A = 25 * 23
A = 575
Now let's try x = 7:
A = (30 - 7)(18 + 7)
A = 23 * 25
A = 575
They both check out.
So we can have

The earth makes a full rotation in 24 hours. Jupiter takes approximately 58 days, 15 h, and 30 min t

The earth makes a full rotation in 24 hours. Jupiter takes approximately 58 days, 15 h, and 30 min to complete a full rotation. How many hours does it take Jupiter to complete a full rotation? Show your work using the correct conversion factors.
Convert 58 days, 15 h, and 30 min to hours.
[LIST=1]
[*]Type [URL='https://www.mathcelebrity.com/timecon.php?quant=58&pl=Calculate&type=day']58 days[/URL] into the search engine to get 1,392 hours.
[*]Add 15 hours to get 1,392 + 15 = 2,007 hours
[*]Now convert the 30 min to hours. [URL='https://www.mathcelebrity.com/timecon.php?quant=30&pl=Calculate&type=minute']Type 30 minutes into the search engine[/URL] to get 0.5 hours
[*]Add up (1), (2), and (3) to get 1,392 + 15 + 0.5 = [B]2007.5[/B] hours for a full rotation.
[/LIST]

The enrollment at High School R has been increasing by 20 students per year. High School R currently

The enrollment at High School R has been increasing by 20 students per year. High School R currently has 200 students. High School T has 400 students and is decreasing 30 students per year. When will the two school have the same enrollment of students?
Set up the Enrollment function E(y) where y is the number of years.
[U]High School R:[/U]
[I]Increasing[/I] means we add
E(y) = 200 + 20y
[U]High School T:[/U]
[I]Decreasing[/I] means we subtract
E(y) = 400 - 30y
When the two schools have the same enrollment, we set the E(y) functions equal to each other
200 + 20y = 400 - 30y
To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=200%2B20y%3D400-30y&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]4[/B]

the equation of a line is y = mx + 4. find m if the line passes through (-5,0)

the equation of a line is y = mx + 4. find m if the line passes through (-5,0)
Plug in our numbers of x = -5, and y = 0:
-5m + 4 = 0
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=-5m%2B4%3D0&pl=Solve']plug in this equation into our search engine[/URL] and we get:
[B]m = 0.8 or 4/5[/B]
so our line equation becomes:
[B]y = 4/5x + 4[/B]

The first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The seco

The first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The second plan had a $21 monthly fee and charges an additional $.10 for each minute of calls. For how many minutes of calls will the cost of the two plans be equal?
Set up the cost equation C(m) for the first plan, where m is the amount of minutes you use
C(m) = 0.14m + 14
Set up the cost equation C(m) for the second plan, where m is the amount of minutes you use
C(m) = 0.10m + 21
Set them equal to each other:
0.14m + 14 = 0.10m + 21
[URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B14%3D0.10m%2B21&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = [B]175[/B]

The fraction has a value of 3/5. The sum of the numerator and the denominator was 40. What was the f

The fraction has a value of 3/5. The sum of the numerator and the denominator was 40. What was the fraction?
We're given two equations with a fraction with numerator (n) and denominator (d):
[LIST=1]
[*]n + d = 40
[*]n/d = 3/5
[/LIST]
Cross multiply equation 2, we get:
5n = 3d
Divide each side by 5:
5n/5 = 3d/5
n = 3d/5
Substitute this into equation 1:
3d/5 + d = 40
Multiply through both sides of the equation by 5:
5(3d/5) = 5d = 40 * 5
3d + 5d =200
To solve this equation for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=3d%2B5d%3D200&pl=Solve']type it in our search engine and we get[/URL]:
d = [B]25
[/B]
Now substitute that back into equation 1:
n + 25 = 40
Using [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B25%3D40&pl=Solve']our equation solver again[/URL], we get:
n = [B]15[/B]

the grass in jamie’s yard grew 16 centimeters in 10 days. how many days did it take for the grass to

the grass in jamie’s yard grew 16 centimeters in 10 days. how many days did it take for the grass to grow 1 centimeter
We set up a proportion of centimeters to days where d is the number of days it takes for the grass to grow 1 centimeter:
16/10 = 1/d
To solve this proportion for d, [URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=1&den1=10&den2=d&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
d = [B]0.625 or 5/8[/B]

The left and right page numbers of an open book are two consecutive integers whose sum is 403. Find

The left and right page numbers of an open book are two consecutive integers whose sum is 403. Find these page numbers.
Page numbers left and right are consecutive integers. So we want to find a number n and n + 1 where:
n + n + 1 = 403
Combining like terms, we get:
2n + 1 = 403
Typing that equation into our search engine, we get:
[B]n = 201[/B]
This is our left hand page. Our right hand page is:
201 + 1 = [B]202[/B]

The length of a rectangle is equal to triple the width. Find the length of the rectangle if the peri

The length of a rectangle is equal to triple the width. Find the length of the rectangle if the perimeter is 80 inches.
The perimeter (P) of a rectangle is:
2l + 2w = P
We're given two equations:
[LIST=1]
[*]l = 3w
[*]2l + 2w = 80
[/LIST]
We substitute equation 1 into equation 2 for l:
2(3w) + 2w = 80
6w + 2w = 80
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D80&pl=Solve']type it in our search engine[/URL] and we get:
w = 10
To solve for the length (l), we substitute w = 10 into equation 1 above:
l = 3(10)
l = [B]30[/B]

The length of a train car is 50.6 feet. This is 5.8 feet less than 6 times the width. What is the wi

The length of a train car is 50.6 feet. This is 5.8 feet less than 6 times the width. What is the width?
l = 50.6
We are also given:
6w - 5.8 = 50.6
[URL='http://www.mathcelebrity.com/1unk.php?num=6w-5.8%3D50.6&pl=Solve']Typing this problem into the search engine[/URL], we get [B]w = 9.4[/B].

The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft²

The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft²
The frame is a rectangle. The area of a rectangle is A = lw. So were given:
[LIST=1]
[*]l = w + 1
[*]lw = 12
[/LIST]
Substitute equation (1) into equation (2) for l:
(w + 1) * w = 12
Multiply through and simplify:
w^2 + w = 12
We have a quadratic equation. To solve for w, we type this equation into our search engine and we get two solutions:
w = 3
w = -4
Since width cannot be negative, we choose the positive result and have:
w = [B]3[/B]
To solve for length, we plug w = 3 into equation (1) above and get:
l = 3 + 1
l = [B]4[/B]

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. Find the dimensions of Sally’s garden.
Gardens have a rectangle shape. Perimeter of a rectangle is 2l + 2w. We're given:
[LIST=1]
[*]l = 3w + 4 [I](3 times the width Plus 4 since greater means add)[/I]
[*]2l + 2w = 72
[/LIST]
We substitute equation (1) into equation (2) for l:
2(3w + 4) + 2w = 72
Multiply through and simplify:
6w + 8 + 2w = 72
(6 +2)w + 8 = 72
8w + 8 = 72
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B8%3D72&pl=Solve']type it in our search engine[/URL] and we get:
w = [B]8
[/B]
To solve for l, we substitute w = 8 above into Equation (1):
l = 3(8) + 4
l = 24 + 4
l = [B]28[/B]

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters
A garden is a rectangle, which has perimeter P of:
P = 2l + 2w
With P = 72, we have:
2l + 2w = 72
We're also given:
l = 3w + 4
We substitute this into the perimeter equation for l:
2(3w + 4) + 2w = 72
6w + 8 + 2w = 72
To solve this equation for w, we t[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B8%2B2w%3D72&pl=Solve']ype it in our search engine[/URL] and we get:
w =[B] 8[/B]
Now, to solve for l, we substitute w = 8 into our length equation above:
l = 3(8) + 4
l = 24 + 4
l = [B]28[/B]

the lowest temperature on may 15 is 2/3 as warm as the warmest temperature on may 15. the lowest tem

the lowest temperature on may 15 is 2/3 as warm as the warmest temperature on may 15. the lowest temperature on may 15 is 60F what is the warmest temperature on may 15?
Set up an equation where w is the warmest temperature on May 15:
60 = 2/3w
[URL='https://www.mathcelebrity.com/1unk.php?num=60%3D2%2F3w&pl=Solve']Type this equation into our search engine[/URL], and we get:
w = [B]90[/B]

The mean age of 5 people in a room is 28 years. A person enters the room. The mean age is now 32. W

The mean age of 5 people in a room is 28 years. A person enters the room. The mean age is now 32. What is the age of the person who entered the room?
The sum of the 5 people's scores is S. We know:
S/5 = 28
Cross multiply:
S = 140
We're told that:
(140 + a)/6 = 32
Cross multiply:
140 + a = 192
[URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D192&pl=Solve']Type this equation into our search engine[/URL], we get:
a = [B]52[/B]

The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. Wh

The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. What is the age of the person who entered the room?
Mean = Sum of Ages in Years / Number of People
32 = Sum of Ages in Years / 5
Cross multiply:
Sum of Ages in Years = 32 * 5
Sum of Ages in Years = 160
Calculate new mean after the next person enters the room.
New Mean = (Sum of Ages in Years + New person's age) / (5 + 1)
Given a new Mean of 40, we have:
40 = (160 + New person's age) / 6
Cross multiply:
New Person's Age + 160 = 40 * 6
New Person's Age + 160 = 240
Let the new person's age be n. We have:
n + 160 = 240
To solve for n, [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B160%3D240&pl=Solve']we type this equation into our search engine[/URL] and we get:
n = [B]80[/B]

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. Wh

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. What is the age of the person who entered the room?
The mean formulas is denoted as:
Mean = Sum of Ages / Total People
We're given Mean = 38 and Total People = 5, so we plug in our numbers:
28 = Sum of Ages / 5
Cross multiply, and we get:
Sum of Ages = 28 * 5
Sum of Ages = 140
One more person enters the room. The mean age is now 39. Set up our Mean formula:
Mean = Sum of Ages / Total People
With a new Mean of 39 and (5 + 1) = 6 people, we have:
39 = Sum of Ages / 6
But the new sum of Ages is the old sum of ages for 5 people plus the new age (a):
Sum of Ages = 140 + a
So we have:
29 = (140 + a)/6
Cross multiply:
140 + a = 29 * 6
140 + a = 174
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D174&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]34[/B]

The mean of 3 numbers is 20. Two of the numbers are 21, and 35. What is the 3rd number?

The mean of 3 numbers is 20. Two of the numbers are 21, and 35. What is the 3rd number?
The mean of 3 numbers is the sum of 3 numbers divided by 3. Let the 3rd number be n. We have:
Mean = (21 + 35 + n) / 3
The Mean is given as 20, so we have:
20 = (n + 56) / 3
Cross multiply:
n + 56 = 20 * 3
n + 56 = 60
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B56%3D60&pl=Solve']type this number in our search engine [/URL]and we get:
n = [B]4[/B]

The mean of two numbers is 49.1. The first number is 18.3. What is the second number

The mean of two numbers is 49.1. The first number is 18.3. What is the second number
We call the second number n. Since the mean is an average, in this case 2 numbers, we have:
(18.3 + n)/2 = 49.1
Cross multiply:
18.3 + n = 98.2
[URL='https://www.mathcelebrity.com/1unk.php?num=18.3%2Bn%3D98.2&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]n = 79.9[/B]

The monthly earnings of a group of business students are are normally distributed with a standard de

The monthly earnings of a group of business students are are normally distributed with a standard deviation of 545 dollars. A researcher wants to estimate the mean monthly earnings of all business students. Find the sample size needed to have a confidence level of 95% and a margin of error of 128 dollars.

The monthly earnings of a group of business students are are normally distributed with a standard de

The monthly earnings of a group of business students are are normally distributed with a standard deviation of 545 dollars. A researcher wants to estimate the mean monthly earnings of all business students. Find the sample size needed to have a confidence level of 95% and a margin of error of 128 dollars.

The ordered pairs (8,12), (16, 24), (x, 21), (26, y ) represent a proportional relationship. Find th

The ordered pairs (8,12), (16, 24), (x, 21), (26, y ) represent a proportional relationship. Find the value of x and the value of y.
12/8 = 1.5
24/16 = 1.5
So we have our proportion; y/x = 1.5 or 3/2
[U]For (x, 21), we have:[/U]
21/x = 3/2
[URL='https://www.mathcelebrity.com/prop.php?num1=21&num2=3&den1=x&den2=2&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get:
x = [B]14[/B]
For (26, y), we have:
y/26 = 3/2
[URL='https://www.mathcelebrity.com/prop.php?num1=y&num2=3&den1=26&den2=2&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get;
y = [B]39[/B]

The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it?

The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it?
[U]Assumptions and givens:[/U]
[LIST]
[*]The poster has a rectangle shape
[*]l = 6
[*]P = 20
[*]The perimeter of a rectangle (P) is: 2l + 2w = P
[/LIST]
Plugging in our l and P values, we get:
2(6) + 2w = 20
Multiplying through and simplifying, we get:
12 + 2w = 20
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B2w%3D20&pl=Solve']type this equation into our search engine [/URL]and we get:
w = [B]4[/B]

The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is

The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is it’s width?
The formula for a rectangles perimeter P, is:
P = 2l + 2w where l is the length and w is the width.
Plugging in our P = 340 and l = 97, we have:
2(97) + 2w = 340
Multiply through, we get:
2w + 194 = 340
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B194%3D340&pl=Solve']Type this equation into our search engine[/URL], we get:
[B]w = 73[/B]

The perimeter of a rectangular field is 220 yd. the length is 30 yd longer than the width. Find the

The perimeter of a rectangular field is 220 yd. the length is 30 yd longer than the width. Find the dimensions
We are given the following equations:
[LIST=1]
[*]220 = 2l + 2w
[*]l = w + 30
[/LIST]
Plug (1) into (2)
2(w + 30) + 2w = 220
2w + 60 + 2w = 220
Combine like terms:
4w + 60 = 220
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B60%3D220&pl=Solve']Plug 4w + 60 = 220 into the search engine[/URL], and we get [B]w = 40[/B].
Now plug w = 40 into equation (2)
l = 40 + 30
[B]l = 70[/B]

The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it’s length

The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it’s length?
Set up the perimeter (P) of a rectangle equation given length (l) and width (w):
2l + 2w = P
We're given P = 300 and w = 59. Plug these into the perimeter equation:
2l + 2(59) = 300
2l + 118 = 300
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B118%3D300&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]l = 91[/B]

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. Wh

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. What are the dimensions of the patio?
Perimeter of a rectangle is:
P = 2l + 2w
We're given l = w + 3 and P = 54. So plug this into our perimeter formula:
54= 2(w + 3) + 2w
54 = 2w + 6 + 2w
Combine like terms:
4w + 6 = 54
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B6%3D54&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 12[/B]
Plug this into our l = w + 3 formula:
l = 12 + 3
[B]l = 15[/B]

The perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, wh

The perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, what is its width?
The perimeter for a rectangle (P) is given as:
2l + 2w = P
We're given P = 258 and l = 71. Plug these values in:
2(71) + 2w = 258
142 + 2w = 258
[URL='https://www.mathcelebrity.com/1unk.php?num=142%2B2w%3D258&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 58[/B]

The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?

The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?
The perimeter for a rectangle is given below:
P = 2l + 2w
We're given l = 7 and P = 60. Plug this into the perimeter formula:
60 = 2(7) + 2w
60 = 14 + 2w
Rewritten, it's 2w + 14 = 60.
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B14%3D60&pl=Solve']Typing this equation into our search engine[/URL], we get [B]w = 23[/B].

The place value of 3 in 16.534 is

The place value of 3 in 16.534 is
We [URL='https://www.mathcelebrity.com/placevalue.php?num=16.534&pl=Show+Place+Value']type in 16.534 into our search engine, choose place value[/URL], and we get:
3 is the [B]hundredths digit[/B]

the ratio of yellow to red balloons is 2:1 respectively. if there are 7 red balloons, how many yello

the ratio of yellow to red balloons is 2:1 respectively. if there are 7 red balloons, how many yellow balloons are there?
7 red balloons means we have twice as many yellow balloons. So 7 * 2 = [B]14[/B].
Written as a proportion, of yellow to red, we have:
2/1 = y/7 where y is the number of yellow balloons.
[URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=y&den1=1&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']Run this proportion through our search engine[/URL] to get [B]y = 14[/B].

the result of quadrupling a number is 80

the result of quadrupling a number is 80
Let our number be x. Quadrupling any number means multiplying it by 4. We have:
4x = 80
[URL='https://www.mathcelebrity.com/1unk.php?num=4x%3D80&pl=Solve']Typing this problem into our search engine[/URL], we get:
[B]x = 20[/B]

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for $40. Write a cost and revenue function and determine the break-even point.
[U]Calculate cost function C(b) with b as the number of books:[/U]
C(b) = Cost per book * b + Overhead
[B]C(b) = 15b + 5500[/B]
[U]Calculate Revenue Function R(b) with b as the number of books:[/U]
R(b) = Sales Price per book * b
[B]R(b) = 40b[/B]
[U]Calculate break even function E(b):[/U]
Break-even Point = Revenue - Cost
Break-even Point = R(b) - C(b)
Break-even Point = 40b - 15b - 5500
Break-even Point = 25b - 5500
[U]Calculate break even point:[/U]
Break-even point is where E(b) = 0. So we set 25b - 5500 equal to 0
25b - 5500 = 0
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-5500%3D0&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]b = 220[/B]

The sides of a triangle are consecutive numbers. If the perimeter of the triangle is 240 m, find the

The sides of a triangle are consecutive numbers. If the perimeter of the triangle is 240 m, find the length of each side
Let the first side be n.
Next side which is consecutive is n + 1
Next side which is consecutive is n + 1 + 1 = n + 2
So we have the sum of 3 consecutive numbers is 240.
We type in [I][URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof3consecutivenumbersis240&pl=Calculate']sum of 3 consecutive numbers is 240[/URL][/I] into our search engine and we get:
[B]79, 80, 81[/B]

The Square of a positive integer is equal to the sum of the integer and 12. Find the integer

The Square of a positive integer is equal to the sum of the integer and 12. Find the integer
Let the integer be x.
[LIST]
[*]The sum of the integer and 12 is written as x + 12.
[*]The square of a positive integer is written as x^2.
[/LIST]
We set these equal to each other:
x^2 = x + 12
Subtract x + 12 from each side:
x^2 - x - 12 = 0
We have a quadratic function. [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2-x-12%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Run it through our search engine[/URL] and we get x = 3 and x = -4.
The problem asks for a positive integer, so we have [B]x = 3[/B]

The sum of 2 consecutive numbers is 3 less than 3 times the first number. What are the numbers?

The sum of 2 consecutive numbers is 3 less than 3 times the first number. What are the numbers?
Let the first number be x. And the second number be y. We're given:
[LIST=1]
[*]y = x + 1
[*]x + y = 3x - 3 (less 3 means subtract 3)
[/LIST]
Substitute (1) into (2):
x + x + 1 = 3x - 3
Combine like terms:
2x + 1 = 3x - 3
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B1%3D3x-3&pl=Solve']Type this equation into the search engine[/URL], we get:
x = 4
Substituting x = 4 into equation 1:
y = 4 + 1
y = 5
So (x, y) = [B](4, 5)[/B]

The sum of 2 numbers is 60. The larger number is thrice the smaller

The sum of 2 numbers is 60. The larger number is thrice the smaller.
Let the 2 numbers be x and y, where x is the smaller number and y is the larger number. We are given:
[LIST=1]
[*]x + y = 60
[*]y = 3x
[/LIST]
Substitute (2) into (1):
x + (3x) = 60
Combine like terms:
4x = 60
[URL='https://www.mathcelebrity.com/1unk.php?num=4x%3D60&pl=Solve']Type 4x = 60 into our search engine[/URL], and you get [B]x = 15[/B].
Substituting x = 15 into Equation (2) above, we get:
y = 3(15)
[B]y = 45
[/B]
Check our work in Equation (1):
15 + 45 ? 60
60 = 60
Check our work in Equation (2):
45 ? 15(3)
45 = 45
The numbers check out, so our answer is [B](x, y) = (15, 45)[/B]

the sum of 23 and victor age is 59

the sum of 23 and victor age is 59
Let's Victor's age be a.
The sum of 23 and Victor's age (a) mean we add a to 23:
23 + a
The word [I]is[/I] means an equation, so we set 23 + a equal to 59:
[B]23 + a = 59[/B] <-- This is our algebraic expression
Now if the problem asks you to take it a step further and solve this for a, [URL='https://www.mathcelebrity.com/1unk.php?num=23%2Ba%3D59&pl=Solve']we type this equation into our search engine[/URL] and we get:
[B]a = 36[/B]

The sum of 3, 7, and a number amounts to 16

The sum of 3, 7, and a number amounts to 16
Let the number be n. A sum means we add. We're given:
3 + 7 + n = 16
Grouping like terms, we get:
n + 10 = 16
[URL='https://www.mathcelebrity.com/1unk.php?num=n%2B10%3D16&pl=Solve']Typing this equation into our search engine[/URL], we get:
n = [B]6 [/B]

the sum of 6 and 7, plus 5 times a number, is -12

the sum of 6 and 7, plus 5 times a number, is -12
The sum of 6 and 7 means we add the two numbers:
6 + 7
This evaluates to 13
Next, we take 5 times a number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So we multiply x by 5:
5x
The first two words say [I]the sum[/I], so we add 13 and 5x
13 + 5x
The word [I]is[/I] means an equation, so we set 13 + 5x equal to -12
[B]13 + 5x = -12[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=13%2B5x%3D-12&pl=Solve']type this algebraic expression into our search engine[/URL] and you get:
[B]x = -5[/B]

the sum of doubling a number and 100 which totals to 160

the sum of doubling a number and 100 which totals to 160
Take this algebraic expression in pieces:
[LIST=1]
[*]Let the number be n.
[*]Double it, means we multiply n by 2: 2n
[*]The sum of this and 100 means we add 100 to 2n: 2n + 100
[*]The phrase [I]which totals[/I] means we set 2n + 100 equal to 160
[/LIST]
[B]2n + 100 = 160[/B] <-- This is our algebraic expression
If the question asks you to solve for n, then we [URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B100%3D160&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]n = 30[/B]

The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age

The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age. How old are they now?
Let Jocelyn's age be a
Let Joseph's age be b.
We're given two equations:
[LIST=1]
[*]a + b = 40
[*]2(a + 5) = b + 5
[/LIST]
We rearrange equation (1) in terms of a to get:
[LIST=1]
[*]a = 40 - b
[*]2a = b + 5
[/LIST]
Substitute equation (1) into equation (2) for a:
2(40 - b) = b + 5
80 - 2b = b + 5
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=80-2b%3Db%2B5&pl=Solve']type it in our search engine[/URL] and we get:
[B]b (Joseph's age) = 25[/B]
Now, substitute b = 25 into equation (1) to solve for a:
a = 40 - 25
[B]a (Jocelyn's age) = 15[/B]

The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages?

The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages?
[U]Givens[/U]
[LIST]
[*]Let Mr. Adam's age be a
[*]Let Mrs. Benson's age be b
[*]We're given two equations where [I]sum[/I] means we add and [I]difference[/I] means we subtract:
[/LIST]
[LIST=1]
[*]a + b = 55
[*]a - b = 3
[/LIST]
Since we have opposite coefficients for b, we can take a shortcut and add equation 1 to equation 2:
(a + a) + (b - b) = 55 + 3
Combining like terms and simplifying, we get:
2a = 58
To solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=2a%3D58&pl=Solve']type it in our search engine[/URL] and we get:
a = [B]29[/B]

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. Ho

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now?
Let Levi's current age be l. Let Renee's current age be r. Were given two equations:
[LIST=1]
[*]l + r = 89
[*]l - 7 = 4(r - 7)
[/LIST]
Simplify equation 2 by multiplying through:
[LIST=1]
[*]l + r = 89
[*]l - 7 = 4r - 28
[/LIST]
Rearrange equation 1 to solve for r and isolate l by subtracting l from each side:
[LIST=1]
[*]r = 89 - l
[*]l - 7 = 4r - 28
[/LIST]
Now substitute equation (1) into equation (2):
l - 7 = 4(89 - l) - 28
l - 7 = 356 - 4l - 28
l - 7 = 328 - 4l
To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l-7%3D328-4l&pl=Solve']type the equation into our search engine[/URL] and we get:
l = [B]67[/B]

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times the unit digit. Find the number.
Let the digits be (x)(y) where t is the tens digit, and o is the ones digit. We're given:
[LIST=1]
[*]x + y = 10
[*]10x+ y = 15y + 4
[/LIST]
Simplifying Equation (2) by subtracting y from each side, we get:
10x = 14y + 4
Rearranging equation (1), we get:
x = 10 - y
Substitute this into simplified equation (2):
10(10 - y) = 14y + 4
100 - 10y = 14y + 4
[URL='https://www.mathcelebrity.com/1unk.php?num=100-10y%3D14y%2B4&pl=Solve']Typing this equation into our search engine[/URL], we get:
y = 4
Plug this into rearranged equation (1), we get:
x = 10 - 4
x = 6
So our number xy is [B]64[/B].
Let's check our work against equation (1):
6 + 4 ? 10
10 = 10
Let's check our work against equation (2):
10(6)+ 4 ? 15(4) + 4
60 + 4 ? 60 + 4
64 = 64

The sum of three numbers is 171. The second number is 1/2 of the first and the third is 3/4 of the f

The sum of three numbers is 171. The second number is 1/2 of the first and the third is 3/4 of the first. Find the numbers.
We have three numbers, x, y, and z.
[LIST=1]
[*]x + y + z = 171
[*]y = 1/2x
[*]z = 3/4x
[/LIST]
Substitute (2) and (3) into (1)
x + 1/2x + 3/4x = 171
Use a common denominator of 4 for each x term
4x/4 + 2x/4 + 3x/4 = 171
(4 + 2 + 3)x/4 = 171
9x/4 = 171
[URL='https://www.mathcelebrity.com/prop.php?num1=9x&num2=171&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Plug this equation into our search engine[/URL], and we get [B]x = 76[/B]
So y = 1/2(76) --> [B]y = 38[/B]
Then z = 3/4(76) --> [B]z = 57[/B]

The team A scored 13 more points than Team B. The total of their score was 47. How many points did t

The team A scored 13 more points than Team B. The total of their score was 47. How many points did team A score?
Let a be the amount of points A scored, and b be the amount of points B scored. We're given:
[LIST=1]
[*]a = b + 13
[*]a + b = 47
[/LIST]
Plug (1) into (2)
(b + 13) + b = 47
Combine like terms:
2b + 13 = 47
[URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B13%3D47&pl=Solve']Typing this equation into our search engine[/URL], we get:
b = 17
Now plug this into (1):
a = 17 + 13
a = [B]30[/B]

The temperature is 68. What is the temperature in degrees Celsius

The temperature is 68. What is the temperature in degrees Celsius
We type [URL='https://www.mathcelebrity.com/temperature.php?temp=68&type=Fahrenheit&pl=Convert']68 degrees Fahrenheit into our search engine[/URL] and we get:
[B]20 Celsius[/B]

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. h

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins?
Let a be Suresh's age, h be Hakima's age, and c be Saad's age. We're given:
[LIST=1]
[*]a + h + c = 48
[*]a = 0.5h
[*]a = c + 4
[/LIST]
To isolate equations in terms of Suresh's age (a), let's do the following:
[LIST]
[*]Rewriting (3) by subtracting 4 from each side, we get c = a - 4
[*]Rewriting (2) by multiply each side by 2, we have h = 2a
[/LIST]
We have a new system of equations:
[LIST=1]
[*]a + h + c = 48
[*]h = 2a
[*]c = a - 4
[/LIST]
Plug (2) and (3) into (1)
a + (2a) + (a - 4) = 48
Group like terms:
(1 + 2 + 1)a - 4 = 48
4a - 4 = 48
[URL='https://www.mathcelebrity.com/1unk.php?num=4a-4%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]a = 13 [/B]<-- Suresh's age
This means that Hakima's age, from modified equation (2) above is:
h = 2(13)
[B]h = 26[/B] <-- Hakima's age
This means that Saad's age, from modified equation (3) above is:
c = 13 - 4
[B]c = 9[/B] <-- Saad's age
[B]
[/B]

The total cost to fix your bike is $45 the parts cost $10 and the labor cost seven dollars per hour

The total cost to fix your bike is $45 the parts cost $10 and the labor cost seven dollars per hour how many hours were there:
Set up a cost function where h is the number of hours:
7h + 10 = 45
To solve for h, we t[URL='https://www.mathcelebrity.com/1unk.php?num=7h%2B10%3D45&pl=Solve']ype this equation into our search engine[/URL] and we get:
h = [B]5[/B]

The value of all the quarters and dimes in a parking meter is $18. There are twice as many quarters

The value of all the quarters and dimes in a parking meter is $18. There are twice as many quarters as dimes. What is the total number of dimes in the parking meter?
Let q be the number of quarters. Let d be the number of dimes. We're given:
[LIST=1]
[*]q = 2d
[*]0.10d + 0.25q = 18
[/LIST]
Substitute (1) into (2):
0.10d + 0.25(2d) = 18
0.10d + 0.5d = 18
[URL='https://www.mathcelebrity.com/1unk.php?num=0.10d%2B0.5d%3D18&pl=Solve']Type this equation into our search engine[/URL], and we get [B]d = 30[/B].

The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2

The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2
The Area (A) of a rectangle is given by:
A = lw
With an area of [I]less than[/I] 86 and a width of 4, we have the following inequality:
4l < 86
To solve for l, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4l%3C86&pl=Show+Interval+Notation']type this inequality into our search engine[/URL] and we get:
[B]l < 21.5[/B]

there are $4.20 in nickel and quarters. There are 6 more nickels than quarters there. How many coins

there are $4.20 in nickel and quarters. There are 6 more nickels than quarters there. How many coins of each are there
We're given two equations:
[LIST=1]
[*]n = q + 6
[*]0.05n + 0.25q = 4.2
[/LIST]
Substitute equation (1) into equation (2):
0.05(q + 6) + 0.25q = 4.2
Multiply through and simplify:
0.05q + 0.3 + 0.25q
0.3q + 0.3 = 4.2
To solve for q, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.3q%2B0.3%3D4.2&pl=Solve']type this equation into the search engine[/URL] and we get:
q = [B]13
[/B]
To solve for n, we plug in q = 13 into equation (1):
n = 13 + 6
n = [B]19[/B]

There are 100 teachers in a school of 3300 students find the ratio of number of teachers to the numb

There are 100 teachers in a school of 3300 students find the ratio of number of teachers to the number of students.
The Ratio is 100/3300.
Divide top and bottom by 100:
1/330 or [B]1:33
[/B]
You can also this into the search engine: [URL='https://www.mathcelebrity.com/ratio.php?simpratio=100%3A3300&rs=+7%3A5&rtot=+36&ab=+7%3A3&bc=+2%3A5&pl=Simplify+Ratio']Ratio of 100 to 3300[/URL].

There are 12 inches per foot. How many inches are there in 14 feet?

There are 12 inches per foot. How many inches are there in 14 feet?
Two ways to solve this. Plug in [URL='http://www.mathcelebrity.com/linearcon.php?quant=14&pl=Calculate&type=foot']14 feet [/URL]into the search engine to get [B]168 inches.[/B]
Or, we do proportions:
12 inches / 1 foot * 14 feet = 12 * 14 = 168 inches per 14 feet.

There are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults?

There are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults?
We set up an equation to represent this:
5x + 3x = 144
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3x%3D144&pl=Solve']Typing this equation into our search engine[/URL], we get:
x = 18
This means we have:
Adults = 5(18)
[B]Adults = 90[/B]
Children = 3(18)
[B]Children = 54[/B]

There are 144 people in the audience. The ratio of adults to children is 5 to 3. How many adults are

[SIZE=6]There are 144 people in the audience. The ratio of adults to children is 5 to 3. How many adults are there?
Let x be the number of people, we have:
5x + 3x = 144
[/SIZE]
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3x%3D144&pl=Solve'][SIZE=6]Typing this problem in our search[/SIZE][/URL][SIZE=6][URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3x%3D144&pl=Solve'] engine[/URL], we get x = 18.
Which means we have 5(18) = [B]90 adults[/B][/SIZE]

There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much

There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much time should we spend sleeping?
3/8 of the day means we take 3/8 of 24 also written as:
3/8 * 24
We [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F8&frac2=24&pl=Multiply']type this expression into our search engine [/URL]and get:
[B]9 hours[/B]

There are 33 students in an Algebra I class. There are 7 fewer girls than boys. How many girls are i

There are 33 students in an Algebra I class. There are 7 fewer girls than boys. How many girls are in the class?
Let b be the number of boys and g be the number of girls. We are given 2 equations:
[LIST=1]
[*]g = b - 7
[*]b + g = 33
[/LIST]
Substitute (1) into (2):
b + (b - 7) = 33
Combine like terms:
2b - 7 = 33
[URL='https://www.mathcelebrity.com/1unk.php?num=2b-7%3D33&pl=Solve']Typing this equation into our search engine[/URL], we get b = 20.
Since the problem asks for how many girls (g) we have, we substitute b = 20 into Equation (1):
g = 20 - 7
[B]g = 13[/B]

There are 40 grams in 5 prunes. How much gram of weight is in 34 prunes

There are 40 grams in 5 prunes. How much gram of weight is in 34 prunes?
Set up a proportion of grams to prunes where g is the number of grams in 34 prunes:
40/5 = g/34
[URL='https://www.mathcelebrity.com/prop.php?num1=40&num2=g&den1=5&den2=34&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion of 40/5 = g/34 into our search engine[/URL], we get:
[B]g = 272[/B]

There are 76 milligrams of cholesterol in a 3.2 ounce serving of lobster. How much cholesterol is in

There are 76 milligrams of cholesterol in a 3.2 ounce serving of lobster. How much cholesterol is in a 6 ounce serving?
Let x equal the amount of cholesterol in milligrams for a 6 ounce service. Set up a proportion:
76/3.2 = x/6
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=76&num2=x&den1=3.2&den2=6&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] by plugging that expression into the search engine, we get x = 142.5

there are some red counters and some yellow counters in the ratio 1:5. There are 20 yellow counters

There are some red counters and some yellow counters in the ratio 1:5. There are 20 yellow counters in the bag.
Set up a proportion where x is the amount of red counters to 20 yellow counters
1/5 = x/20
Enter that in the search engine and our [URL='http://www.mathcelebrity.com/prop.php?num1=1&num2=x&den1=5&den2=20&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] gives us:
[B]x = 4[/B]

There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The

There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The difference between 2 times the first number and 3 times the second number is 24. Find the two numbers.
Let the first number be x and the second number be y. We have 2 equations:
[LIST=1]
[*]4x + 3y = 24
[*]2x - 3y = 24
[/LIST]
Without doing anything else, we can add the 2 equations together to eliminate the y term:
(4x + 2x) + (3y - 3y) = (24 + 24)
6x = 48
Divide each side by 6:
[B]x = 8
[/B]
Substitute this into equation (1)
4(8) + 3y = 24
32 + 3y = 24
[URL='https://www.mathcelebrity.com/1unk.php?num=32%2B3y%3D24&pl=Solve']Type 32 + 3y = 24 into our search engine[/URL] and we get [B]y = 2.6667[/B].

There is a sales tax of $4 on an item that cost $54 before tax. The sales tax on a second item is $1

There is a sales tax of $4 on an item that cost $54 before tax. The sales tax on a second item is $14. How much does the second item cost before tax?
Sales Tax on First Item = Tax Amount / Before Tax Sale Amount
Sales Tax on First Item = 4/54
Sales Tax on First Item = 0.07407407407
For the second item, let the before tax sale amount be b. We have:
0.07407407407b = 14
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.07407407407b%3D14&pl=Solve']type it in our search engine[/URL] and we get:
b = [B]189[/B]

There is an escalator that is 1090.3 feet long and drops a vertical distance of 193.4 feet. What is

There is an escalator that is 1090.3 feet long and drops a vertical distance of 193.4 feet. What is its angle of depression?
The sin of the angle A is the length of the opposite side / hypotenuse.
sin(A) = Opposite / Hypotenuse
sin(A) = 193.4 / 1090/3
sin(A) = 0.1774
[URL='https://www.mathcelebrity.com/anglebasic.php?entry=0.1774&pl=arcsin']We want the arcsin(0.1774)[/URL].
[B]A = 10.1284[/B]

Three good friends are in the same algebra class, their scores on a recent test are three consecutiv

Three good friends are in the same algebra class, their scores on a recent test are three consecutive odd integers whose sum is 273. Find the score
In our search engine, we type in [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=3consecutiveintegerswhosesumis273&pl=Calculate']3 consecutive integers whose sum is 273[/URL] and we get:
[B]90, 91, 92[/B]

To be a member of world fitness gym, it costs $60 flat fee and $30 per month. Maria has paid a total

To be a member of world fitness gym, it costs $60 flat fee and $30 per month. Maria has paid a total of $210 for her gym membership so far. How long has Maria been a member to the gym?
The cost function C(m) where m is the number of months for the gym membership is:
C(m) = 30m + 60
We're given that C(m) = 210 for Maria. We want to know the number of months (m) that Maria has been a member.
With C(m) = 210, we have:
30m + 60 =210
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=30m%2B60%3D210&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]5[/B]

To rent a building for a school dance, Ava paid 120 plus 2.50 for each student. To attend the school

To rent a building for a school dance, Ava paid 120 plus 2.50 for each student. To attend the school all together Ava paid 325. How many students attended the dance?
Let the number of students be s. We're given
2.50s + 120 = 325
[URL='https://www.mathcelebrity.com/1unk.php?num=2.50s%2B120%3D325&pl=Solve']Type this equation into our search engine[/URL], and we get:
s = [B]82[/B]

To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional po

To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional pound. To ship a package with FedEx, the cost will be $5 for the first pound and $0.30 for each additional pound. How many pounds will it take for UPS and FedEx to cost the same? If you needed to ship a package that weighs 8 lbs, which shipping company would you choose and how much would you pay?
[U]UPS: Set up the cost function C(p) where p is the number of pounds:[/U]
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.2(p - 1) + 7
[U]FedEx: Set up the cost function C(p) where p is the number of pounds:[/U]
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.3(p - 1) + 5
[U]When will the costs equal each other? Set the cost functions equal to each other:[/U]
0.2(p - 1) + 7 = 0.3(p - 1) + 5
0.2p - 0.2 + 7 = 0.3p - 0.3 + 5
0.2p + 6.8 = 0.3p + 4.7
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B6.8%3D0.3p%2B4.7&pl=Solve']type it in our search engine[/URL] and we get:
p = [B]21
So at 21 pounds, both UPS and FedEx costs are equal
[/B]
Now, find out which shipping company has a better rate at 8 pounds:
[U]UPS:[/U]
C(8) = 0.2(8 - 1) + 7
C(8) = 0.2(7) + 7
C(8) = 1.4 + 7
C(8) = 8.4
[U]FedEx:[/U]
C(8) = 0.3(8 - 1) + 5
C(8) = 0.3(7) + 5
C(8) = 2.1 + 5
C(8) = [B]7.1[/B]
[B]Therefore, FedEx is the better cost at 8 pounds since the cost is lower[/B]
[B][/B]

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one yea

Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now. Given that my age is an integer number of years, what is the smallest my age could be?
Let my current age be a. We're given:
4/5a > 3/4(a + 1)
Multiply through on the right side:
4a/5 > 3a/4 + 3/4
Let's remove fractions by multiply through by 5:
5(4a/5) > 5(3a/4) + 5(3/4)
4a > 15a/4 + 15/4
Now let's remove the other fractions by multiply through by 4:
4(4a) > 4(15a/4) + 4(15/4)
16a > 15a + 15
[URL='https://www.mathcelebrity.com/1unk.php?num=16a%3E15a%2B15&pl=Solve']Typing this inequality into our search engine[/URL], we get:
a > 15
This means the smallest [I]integer age[/I] which the problem asks for is:
15 + 1 = [B]16[/B]

Tomás is a salesperson who earns a monthly salary of $2250 plus a 3% commission on the total amount

Tomás is a salesperson who earns a monthly salary of $2250 plus a 3% commission on the total amount of his sales. What were his sales last month if he earned a total of $4500?
Let total sales be s. We're given the following earnings equation:
0.03s + 2250 = 4500
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.03s%2B2250%3D4500&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]75,000[/B]

Tony has 6 cds that he is giving away. He lets his best friend choose 3 of the 6 cds. How many gr

Tony has 6 cds that he is giving away. He lets his best friend choose 3 of the 6 cds. How many groups of 3 cds are possible?
This problem asks for [I]unique[/I] combinations. We want 6 choose 3, or 6C3.
Go to the [URL='https://www.mathcelebrity.com/permutation.php?num=6&den=3&pl=Combinations']search engine, and type in 6C3[/URL], we get [B]20[/B] possible groups.

Trig Measurement

Given an angle θ, this calculates the following measurements:

Sin(θ) = Sine

Cos(θ) = Cosine

Tan(θ) = Tangent

Csc(θ) = Cosecant

Sec(θ) = Secant

Cot(θ) = Cotangent

Arcsin(x) = θ = Arcsine

Arccos(x) = θ = Arccosine

Arctan(x) =θ = Arctangent

Also converts between Degrees and Radians and Gradians

Coterminal Angles as well as determine if it is acute, obtuse, or right angle. For acute angles, a cofunction will be determined. Also shows the trigonometry function unit circle

Sin(θ) = Sine

Cos(θ) = Cosine

Tan(θ) = Tangent

Csc(θ) = Cosecant

Sec(θ) = Secant

Cot(θ) = Cotangent

Arcsin(x) = θ = Arcsine

Arccos(x) = θ = Arccosine

Arctan(x) =θ = Arctangent

Also converts between Degrees and Radians and Gradians

Coterminal Angles as well as determine if it is acute, obtuse, or right angle. For acute angles, a cofunction will be determined. Also shows the trigonometry function unit circle

Twelve students tried out for the football team. Coach Moorhead only has 5 openings. In how many way

Twelve students tried out for the football team. Coach Moorhead only has 5 openings. In how many ways, can he pick 5 of the 12 students to be on the team?
We use the combinations formula. We can write this as 12C5. [URL='https://www.mathcelebrity.com/permutation.php?num=12&den=5&pl=Combinations']Type this into our search engine[/URL] and we get:
[B]792 ways[/B]

Two numbers that total 44 and have a difference of 6

Two numbers that total 44 and have a difference of 6.
Let the two numbers be x and y. We're given the following equations:
[LIST=1]
[*]x + y = 44 <-- Total means a sum
[*]x - y = 6
[/LIST]
Add the two equations together:
(x + x) + (y - y) = 44 + 6
Cancelling the y terms, we have:
2x = 50
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D50&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]x = 25
[/B]
Rearranging equation (2) above, we get:
y = x - 6
Substituting x = 25 into this, we get:
y = 25 - 6
[B]y = 19[/B]

Two numbers total 12, and their differences is 20. Find the two numbers.

Two numbers total 12, and their differences is 20. Find the two numbers.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x + y = 12
[*]x - y = 20
[/LIST]
Since we have y coefficients of (-1 and 1) that cancel, we add the two equations together:
(x + x) + (y - y) = 12 + 20
The y terms cancel, so we have:
2x = 32
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D32&pl=Solve']Type this equation into our search engine[/URL] and we get:
x = [B]16[/B]
Substitute this value of x = 16 back into equation 1:
16 + y = 12
[URL='https://www.mathcelebrity.com/1unk.php?num=16%2By%3D12&pl=Solve']Typing this equation into our search engine[/URL], we get:
y = [B]-4
[/B]
Now, let's check our work for both equations:
[LIST=1]
[*]16 - 4 = 12
[*]16 - -4 --> 16 + 4 = 20
[/LIST]
So these both check out.
(x, y) = ([B]16, -4)[/B]

two pages that face each other in a book have a sum of 569

two pages that face each other in a book have a sum of 569
Pages that face each other are consecutive. Let the first page be p. The second page is p + 1.
Their sum is:
p + p + 1 = 569
[URL='https://www.mathcelebrity.com/1unk.php?num=p%2Bp%2B1%3D569&pl=Solve']Type this equation into our search engine to solve for p[/URL], and we get:
p = 284
This means p + 1 = 284 + 1 = 285
So the pages that face each other having a sum of 569 are:
[B]284, 285[/B]

Tyler has a meal account with $1200 in it to start the school year. Each week he spends $21 on food

Tyler has a meal account with $1200 in it to start the school year. Each week he spends $21 on food
a.) write an equation that relates the amount in the account (a) with the number of (w) weeks
b.) How many weeks will it take until Tyler runs out of money?
[U]Part a) where w is the number of weeks[/U]
a = Initial account value - weekly spend * w ([I]we subtract because Tyler spends)[/I]
a = [B]1200 - 21w
[/B]
[U]Part b)[/U]
We want to know the number of weeks it takes where a = 0. So we have:
1200 - 21w = 0
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=1200-21w%3D0&pl=Solve']type this equation into our search engine[/URL] and we get:
w = 57.14 weeks
The problem asks for when he runs out of money, so we round up to [B]58 whole weeks[/B]

Unit Cost Calculator

I just created a new [URL='http://www.mathcelebrity.com/unit-cost-calculator.php']unit cost calculator[/URL]. As more searches come in, I'll add more shortcuts.
First type of shortcut:
3 pound bag for $11.25

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.
Let Victoria's age be v. And her neighbor's age be n. We're given:
[LIST=1]
[*]v = n + 4
[*]v + n <=14 <-- no more than means less than or equal to
[/LIST]
Substitute Equation (1) into Inequality (2):
(n + 4) + n <= 14
Combine like terms:
2n + 4 <= 14
[URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B4%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get:
n <= 5
Substituting this into inequality (2):
v + 5 <= 14
[URL='https://www.mathcelebrity.com/1unk.php?num=v%2B5%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]v <= 9[/B]

What fraction lies exactly halfway between 2/3 and 3/4?

What fraction lies exactly halfway between 2/3 and 3/4?
A) 3/5
B) 5/6
C) 7/12
D) 9/16
E) 17/24
Halfway means taking the average, which is dividing the sum of the fractions by 2 for 2 fractions:
1/2(2/3 + 3/4)
1/2(2/3) + 1/2(3/4)
1/3 + 3/8
We need common denominators, so [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F3&frac2=3%2F8&pl=Add']we type this fraction sum into our search engine[/URL] and get:
[B]17/24 - Answer E[/B]

what integer is tripled when 9 is added to 3 fourths of it?

what integer is tripled when 9 is added to 3 fourths of it?
Let the integer be n. Tripling an integer means multiplying it by 3. We're given:
3n = 3n/4 + 9
Since 3 = 12/4, we have:
12n/4 = 3n/4 + 9
Subtract 3n/4 from each side:
9n/4 = 9
[URL='https://www.mathcelebrity.com/prop.php?num1=9n&num2=9&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this equation into the search engine[/URL], we get:
[B]n = 4[/B]

What is the correct translation of; 8 increased by a number is 10?

What is the correct translation of; 8 increased by a number is 10?
We [URL='https://www.mathcelebrity.com/community/forums/calculator-requests.7/create-thread']type in [I]8 increased by a number is 10[/I] into our search engine[/URL] and we get:
[B]8 + a = 10[/B]

What is the probability that a month chosen at random has less than 31 days?

What is the probability that a month chosen at random has less than 31 days?
Months with 31 days:
[LIST=1]
[*]January
[*]March
[*]May
[*]July
[*]August
[*]October
[*]December
[/LIST]
7 months out of 12 have 31 days, so our probability is [B]7/12[/B]

what is the probabilty of tossing two coins and both landing on heads

what is the probabilty of tossing two coins and both landing on heads
We want P(HH). We type in [URL='https://www.mathcelebrity.com/cointoss.php?hts=HH&hct=+2&tct=+1&fct=+5>=no+more+than&nmnl=+2&htpick=tails&calc=1&montect=500&pl=Calculate+Probability']HH into our search engine[/URL] and we get:
P(HH) = [B]0.25 or 1/4[/B]

What pair of factors of -28 has a sum of -3

What pair of factors of -28 has a sum of -3?
We type in [I]factor -28[/I] into our search engine.
Scrolling down the list of factor sums, we see:
-7 + 4 = -3
So our answer is [B](-7, 4)[/B]

WHAT SHOULD BE SUBTRACTED FROM -9876 TO OBTAIN -9512

WHAT SHOULD BE SUBTRACTED FROM -9876 TO OBTAIN -9512
We set up an arbitrary number x.
Subtracted from is written as
-9876 - x
The phrase [I]to obtain[/I] means an equation, so we set -9876 - x equal to -9512
-9876 - x = -9512
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=-9876-x%3D-9512&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]364[/B]

When 39 is added to a number, the result is 40 times the number. Find the number. Let n be the unkn

When 39 is added to a number, the result is 40 times the number. Find the number. Let n be the unknown number. Write the translated equation below.
[LIST=1]
[*]39 added to a number is written as n + 39
[*]40 times the number is written as 40n
[*]The result is means we have an equation, so set (1) equal to (2)
[/LIST]
n+ 39 = 40n
Running [URL='http://www.mathcelebrity.com/1unk.php?num=n%2B39%3D40n&pl=Solve']n + 39 = 40n through the search engine[/URL], we get[B] n = 1[/B].

When 4 is subtracted from the square of a number, the result is 3 times the number. Find the positiv

When 4 is subtracted from the square of a number, the result is 3 times the number. Find the positive solution.
Let the number be n. We have:
n^2 - 4 = 3n
Subtract 3n from each side:
n^2 - 3n - 4 = 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-3n-4%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Typing this quadratic equation into the search engine[/URL], we get:
n = (-1, 4)
The problem asks for the positive solution, so we get [B]n = 4[/B].

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the num

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. Find the number
The phrase [I]a number, [/I]means an arbitrary variable, let's call it "x".
4 times a number, increased by 40, means we multiply 4 times x, and then add 40
4x + 40
100 decreased by the number means we subtract x from 100
100 - x
The problem tells us both of these expressions are the same, so we set them equal to each other:
4x + 40 = 100 - x
Add x to each side:
4x + x + 40 = 100 - x + x
The x's cancel on the right side, so we have:
5x + 40 = 100
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B40%3D100&pl=Solve']Typing this equation into the search engine[/URL], we get [B]x = 12[/B].

When 9 is subtracted from 5 times a number ,the result is 31

When 9 is subtracted from 5 times a number ,the result is 31
A number means an arbitrary variable, let's call it x.
5 times this number is written as 5x.
9 subtracted from this is written as 5x - 9
[I]The result[/I] means we have an equation, so we set [B]5x - 9 = 31[/B]. This is our algebraic expression.
Now if we want to solve for x, we [URL='http://www.mathcelebrity.com/1unk.php?num=5x-9%3D31&pl=Solve']plug this equation into the search engine [/URL]and get [B]x = 8[/B].

When a number is doubled, the result is 36

Excited to announce these types of algebraic expressions can be [URL='http://www.mathcelebrity.com/algexpress.php?num=whenanumberisdoubled,theresultis36&pl=Write+Expression']typed directly in our search engine[/URL].

When twice a number is reduced by 15 you get 95 what is the number

When twice a number is reduced by 15 you get 95 what is the number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
[I]Twice[/I] x means we multiply x by 2
2x
[I]Reduced by[/I] 15 means we subtract 15
2x - 15
[I]You get[/I] means equal to, as in an equation. Set 2x - 15 = 95
2x - 15 = 95 <-- This is our algebraic expression.
[URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D95&pl=Solve']Type 2x - 15 = 95 into the search engine[/URL] and we get [B]x = 55[/B].

Which of the following descriptions of null hypothesis are correct? (Select all that apply) a. A nu

Which of the following descriptions of null hypothesis are correct? (Select all that apply)
a. A null hypothesis is a hypothesis tested in significance testing.
b. The parameter of a null hypothesis is commonly 0.
c. The aim of all research is to prove the null hypothesis is true
d. Researchers can reject the null hypothesis if the P-value is above 0.05
[B]a. A null hypothesis is a hypothesis tested in significance testing.
[/B]
[I]b. is false because a parameter can be anything we choose it to be
c. is false because our aim is to disprove or fail to reject the null hypothesis
d. is false since a p-value [U]below[/U] 0.05 is often the rejection level.[/I]

Wilbie had candy to give to his 3 children. He first took 5 pieces and evenly divided the rest among

Wilbie had candy to give to his 3 children. He first took 5 pieces and evenly divided the rest among each child. Each child received 3 pieces. With how many pieces did he start?
Let the starting candy amount be c. We're given:
(c - 5)/3 = 3
Cross multiply:
c - 5 = 3*3
c - 5 = 9
[URL='https://www.mathcelebrity.com/1unk.php?num=c-5%3D9&pl=Solve']Type this equation into the search engine[/URL], and we get:
c = 14

write an algebraic expression for 197 times y

write an algebraic expression for 197 times y
[B]197y
[/B]
This can also be found by typing 197 times y into our search engine

Write the interval (2,5) in set builder notation

Write the interval (2,5) in set builder notation
It's a closed interval, so [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=%5B2%2C5%5D&pl=Show+Interval+Notation']we type in [2,5] into the search engine[/URL], and we get:
[B]{x|2<= x <= 5}[/B]

Write the verbal expression for: 9x

You can now add shortcuts in the search engine for this.

X is not between 6 and 12

You can now type in to the search engine directly, X is not between 6 and 12

X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4

X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4
Varies directly means there is a constant k such that:
x = ky^(1/3)
When x = 1 and y = 27, we have:
27^1/3(k) = 1
3k = 1
To solve for k, we[URL='https://www.mathcelebrity.com/1unk.php?num=3k%3D1&pl=Solve'] type in our equation into our search engine[/URL] and we get:
k = 1/3
Now, the problem asks for y when x = 4. We use our variation equation above with k = 1/3 and x = 4:
4 = y^(1/3)/3
Cross multiply:
y^(1/3) = 4 * 3
y^(1/3) =12
Cube each side:
y^(1/3)^3 = 12^3
y = [B]1728[/B]

You are baking muffins for your class. There are 17 total students in your class and you have baked

You are baking muffins for your class. There are 17 total students in your class and you have baked 5 muffins. Write and solve an equation to find the additional number x of muffins you need to bake in order to have 2 muffins for each student. Write your equation so that the units on each side of the equation are muffins per student.
2 muffins per student = 17*2 = 34 muffins.
We have an equation with a given 5 muffins, how much do we need (x) to get to 34 muffins (2 per student):
x + 5 = 34
To solve for x, we type this equation into our search engine and we get:
x = [B]29[/B]

You are baking muffins for your class. There are 17 total students in your class and you have baked

You are baking muffins for your class. There are 17 total students in your class and you have baked 5 muffins. Write and solve an equation to find the additional number x of muffins you need to bake in order to have 2 muffins for each student. Write your equation so that the units on each side of the equation are muffins per student.
[U]Calculate total muffins:[/U]
Total muffins = 2 muffins per student * 17 students
Total muffins = 34
[U]Set up the equation using x for muffins:[/U]
[B]x + 5 = 34
[/B]
[U]To Solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B5%3D34&pl=Solve']type it in our search engine[/URL] and we get:[/U]
x = [B]29
[/B]

You are researching the price of DVD players. You found an average price of $58.80. One DVD player c

You are researching the price of DVD players. You found an average price of $58.80. One DVD player costs $56 and another costs $62. Find the price of the third DVD player.
We want to find n, such that n makes the average of the 3 DVD players $58.80.
[URL='https://www.mathcelebrity.com/missingaverage.php?num=56%2C62&avg=58.80&pl=Calculate+Missing+Score']Using our missing average calculator[/URL], we get the price of the 3rd DVD player is $58.40.

You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase

You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase is $19.08, which includes 6% sales tax. Write and solve an equation to find the cost of the cat food.
Our purchase includes at cat litter and cat food. Adding those together, we're given:
12.25 + x = 19.08
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=12.25%2Bx%3D19.08&pl=Solve']we type this equation into our search engine[/URL], and we get:
x = 6.83
Since the cat food includes sales tax, we need to remove the sales tax of 6% to get the original purchase price.
Original purchase price = After tax price / (1 + tax rate)
Original purchase price = 6.83/1.06
Original purchase price = [B]$6.44[/B]

You can get 2 different moving companies to help you move. The first one charges $150 up front then

You can get 2 different moving companies to help you move. The first one charges $150 up front then $38 an hour. The second one charges $230 then $30 an hour, at what exact time will Both companies cost the same
[U]Company 1: We set up the cost equation C(h) where h is the number of hours[/U]
C(h) = Hourly Rate * h + up front charge
C(h) = 38h + 150
[U]Company 2: We set up the cost equation C(h) where h is the number of hours[/U]
C(h) = Hourly Rate * h + up front charge
C(h) = 30h + 230
The question asks for h when both cost equations C(h) are equal. So we set both C(h) equations equal to other:
38h + 150 = 30h + 230
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=38h%2B150%3D30h%2B230&pl=Solve']type this equation into our search engine [/URL]and we get:
h = [B]10[/B]

You can spend at most $35. If you buy 5 tickets, how much can you spend on each ticket

You can spend at most $35. If you buy 5 tickets, how much can you spend on each ticket
We're given the number of tickets as 5.
We know cost = price * quantity
Let p = price
The phrase [B]at most[/B] means less than or equal to, so we have:
5p <= 35
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=5p%3C%3D35&pl=Show+Interval+Notation']Plugging this inequality into our search engine[/URL], we have:
[B]p <= 7[/B]

You earned $141 last week babysitting and cleaning. You earned $5 per hour babysitting and $7 per ho

You earned $141 last week babysitting and cleaning. You earned $5 per hour babysitting and $7 per hour cleaning. You worked 9 more hours babysitting than cleaning. How many hours did you work last week?
Let b be the hours of babysitting and c be the hours of cleaning. We're given two equations:
[LIST=1]
[*]b = c + 9
[*]5b + 7c = 141
[/LIST]
Substitute equation (1) into (2):
5(c + 9) + 7c = 141
Multiply through:
5c + 45 + 7c = 141
Combine like terms:
12c + 45 = 141
[URL='https://www.mathcelebrity.com/1unk.php?num=12c%2B45%3D141&pl=Solve']Typing this equation into our search engine[/URL], we get:
c = 8
Now substitute this value of c back into Equation (1):
b = 8 + 9
b = 17
The total hours worked (t) is:
t = b + c
t = 17 + 8
t = [B]25[/B]

You have $140 in a savings account and save $10 per week. Your friend has $95 in a savings account a

You have $140 in a savings account and save $10 per week. Your friend has $95 in a savings account and saves $19 per week. How many weeks will it take for you and your friend to have the same balance?
[U]Set up the savings account S(w) for you where w is the number of weeks[/U]
S(w) = 140 + 10w
[U]Set up the savings account S(w) for your friend where w is the number of weeks[/U]
S(w) = 95 + 19w
The problem asks for the number of weeks (w) when the balances are the same. So set both equations equal to each other:
140 + 10w = 95 + 19w
To solve this equation for w, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2B10w%3D95%2B19w&pl=Solve']we type it in the search engine[/URL] and get:
w = [B]5[/B]

You have $6.50 to make copies. It cost $0.45. Write and solve an equality that represents the number

You have $6.50 to make copies. It cost $0.45. Write and solve an equality that represents the number of copies
Hoow many exact copies can you make? Let the number of copies be c. We have:
0.45c = 6.50
[URL='https://www.mathcelebrity.com/1unk.php?num=0.45c%3D6.50&pl=Solve']Type this equation into our search engine[/URL] and we get:
c = 14.444
We round down and say we can make 14 copies.
[B]c = 14[/B]
Now, if the problem asks you for an [I]inequality[/I], we want to see how many copies we can make without exceeding our $6.50 spend. So it's less than or equal to:
[B]c <= 14[/B]

You have 4 dimes, 1 quarter and 6 pennies. How many cents do you have? Write it as a decimal

You have 4 dimes, 1 quarter and 6 pennies. How many cents do you have? Write it as a decimal
We type in [URL='https://www.mathcelebrity.com/coinvalue.php?p=6&n=&d=4&q=1&h=&dol=&pl=Calculate+Coin+Value']4 dimes, 1 quarter, 6 pennies into our search engine[/URL] and we get:
[B]0.71 as a decimal for cents[/B]

You have to pay 29 a month until you reach 850 how many months will that take

You have to pay 29 a month until you reach 850 how many months will that take.
Let m be the number of months. We set up the inequality:
29m > = 850 <-- We want to know when we meet or exceed 850, so we use greater than or equal to
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=29m%3E%3D850&pl=Show+Interval+Notation']Type this inequality into our search engine[/URL], and we get:
m >= 29.31
We round up to the next integer month, to get [B]m = 30[/B].

You receive 9 text messages in 12 minutes. What is the rate of text messages per hour?

You receive 9 text messages in 12 minutes. What is the rate of text messages per hour?
Set up a proportion of text messages to minutes. Remember, there are 60 minutes in an hour, so we have:
9/12 = t/60 where t is the number of text messages in 60 minutes (1 hour)
[URL='https://www.mathcelebrity.com/prop.php?num1=9&num2=t&den1=12&den2=60&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this into the search engine[/URL], we get [B]t = 45[/B].

You spend $91 shopping for new clothes. You spend $24 for a pair of jeans and 35$ for a pair of shoe

You spend $91 shopping for new clothes. You spend $24 for a pair of jeans and 35$ for a pair of shoes. You also buy 4 shirts that cost d dollars. How much is each shirt?
Subtract the cost of the jeans and shoes to get the cost of the shirts:
Cost of shirts = Shopping Spend - Cost of Jeans - Cost of Shoes
Cost of shirts = $91 - $24 - $35
Cost of shirts = $32
We're given the cost of each shirt is s, and we bought 4 shirts. Therefore, we have:
4s = 32
[URL='https://www.mathcelebrity.com/1unk.php?num=4s%3D32&pl=Solve']Type this equation into the search engine[/URL], and we get the cost of each shirt s = [B]$8[/B]

Your friends in class want you to make a run to the vending machine for the whole group. Everyone pi

Your friends in class want you to make a run to the vending machine for the whole group. Everyone pitched in to make a total of $12.50 to buy snacks. The fruit drinks are $1.50 and the chips are $1.00. Your friends want you to buy a total of 10 items. How many drinks and how many chips were you able to purchase?
Let c be the number of chips. Let f be the number of fruit drinks. We're given two equations:
[LIST=1]
[*]c + f = 10
[*]c + 1.5f = 12.50
[/LIST]
Rearrange equation 1 by subtracting f from both sides:
[LIST=1]
[*]c = 10 - f
[*]c + 1.5f = 12.50
[/LIST]
Substitute equation (1) into equation (2):
10 - f + 1.5f = 12.50
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=10-f%2B1.5f%3D12.50&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]f = 5[/B]
Now, substitute this f = 5 value back into modified equation (1) above:
c = 10 - 5
[B]c = 5[/B]

Your mother gave you $13.32 With which to buy a present. This covered 3/5 of the cost. How much did

Your mother gave you $13.32 With which to buy a present. This covered 3/5 of the cost. How much did the present cost
Let the present cost p. We set up the equation we're given:
3/5p = 13.32
[URL='https://www.mathcelebrity.com/1unk.php?num=3%2F5p%3D13.32&pl=Solve']Type this equation into our search engine[/URL] and we get:
p = [B]$22.20[/B]

your starting salary at a new company is 45000. Each year you receive a 2% raise. How long will it t

your starting salary at a new company is 45000. Each year you receive a 2% raise. How long will it take you to make $80000?
Let y be the number of years of compounding the 2% raise. Since 2% as a decimal is 0.02, we have the following equation for compounding the salary:
45000 * (1.02)^y = 80000
Divide each side by 45000:
(1.02)^y = 1.77777777778
To solve this equation for y, we [URL='https://www.mathcelebrity.com/natlog.php?num=1.02%5Ey%3D1.77777777778&pl=Calculate']type it in our search engine[/URL] and we get:
y = [B]29.05[/B]
[B]Or just over 29 years[/B]

z varies jointly as x and y. If z=3 when x=3 and y=15, find z when x=6 and y=9

z varies jointly as x and y. If z=3 when x=3 and y=15, find z when x=6 and y=9
Varies jointly means there exists a constant k such that:
z = kxy
We're given z = 3 when x = 3 and y = 15, so we have:
3 = 15 * 3 * k
3 = 45k
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=3%3D45k&pl=Solve']equation solver,[/URL] we see that:
k = 1/15
So our joint variation equation is:
z = xy/15
Then we're asked to find z when x = 6 and y = 9
z = 6 * 9 / 15
z = 54/15
[URL='https://www.mathcelebrity.com/search.php?q=54%2F15&x=0&y=0']z =[/URL] [B]18/5[/B]

Zach can read 7 pages of a book in 5 minutes. At this rate, how long will it take him to read the en

Zach can read 7 pages of a book in 5 minutes. At this rate, how long will it take him to read the entire 175 page book?
Set up a proportion of pages to minutes where m is the number of minutes needed to read 175 pages:
7/5 = 175/m
To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=7&num2=175&den1=5&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine [/URL]and we get:
m = [B]125 minutes or 2 hours and 5 minutes[/B]

Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same a

Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same as subtracting 5 from the number then multiplying by 4.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We're given two expressions in relation to this number (x):
[U]She subtracts 6 then multiplies the result by 5[/U]
[LIST]
[*]Subtract 6: x - 6
[*]Multiply the result by 5: 5(x - 6)
[/LIST]
[U]She subtracts 5 from the number then multiplying by 4[/U]
[LIST]
[*]Subtract 6: x - 5
[*]Multiply the result by 5: 4(x - 5)
[/LIST]
Finally, the expression [I]is the same as[/I] means an equation, so we set the first expression equal to the second expression to make the following equation:
5(x - 6) = 4(x - 5)
Now, let's solve the equation for x. To do this, we [URL='https://www.mathcelebrity.com/1unk.php?num=5%28x-6%29%3D4%28x-5%29&pl=Solve']type this equation into our search engine [/URL]and we get:
x = [B]10[/B]