given - A thing or set of things helpful in forming a conclusion or judgment

$1,100 per month for 10 years, if the account earns 2% per year

$1,100 per month for 10 years, if the account earns 2% per year
What the student or parent is asking is: If they deposit $1,100 per month in a savings/investment account every month for 10 years, and they earn 2% per year, how much will the account be worth after 10 years?
Deposits are monthly. But interest crediting is annual. What we want is to match the two based on interest crediting time, which is annual or yearly.
1100 per month. * 12 months in a year = 13,200 per year in deposit
Since we matched interest crediting period with deposits, we now want to know:
If they deposit $13,200 per year in a savings/investment account every year for 10 years, and they earn 2% per year, how much will the account be worth after 10 years?
This is an annuity, which is a constant stream of payments with interest crediting at a certain period.
[SIZE=5][B]Calculate AV given i = 0.02, n = 10[/B]
[B]AV = Payment * ((1 + i)^n - 1)/i[/B][/SIZE]
[B]AV =[/B]13200 * ((1 + 0.02)^10 - 1)/0.02
[B]AV =[/B]13200 * (1.02^10 - 1)/0.02
[B]AV =[/B]13200 * (1.2189944199948 - 1)/0.02
[B]AV =[/B]13200 * 0.21899441999476/0.02
[B]AV = [/B]2890.7263439308/0.02
[B]AV = 144,536.32[/B]

$3.75 in quarters and nickles in her car. The number of nickles is fifteen more than the number of q

$3.75 in quarters and nickels in her car. The number of nickels is fifteen more than the number of quarters. How many of each type of coin does she have?
Let the number of nickels be n, and the number of quarters be q. We know nickels are 0.05, and quarters are 0.25. We're given:
[LIST=1]
[*]n = q + 15
[*]0.05n + 0.25q = 3.75
[/LIST]
Substituting (1) into (2), we get:
0.05(q + 15) + 0.25q = 3.75
0.05q + 0.75 + 0.25q = 3.75
Combine like term:
0.3q + 0.75 = 3.75
[URL='https://www.mathcelebrity.com/1unk.php?num=0.3q%2B0.75%3D3.75&pl=Solve']Typing this equation into our calculator[/URL], we get:
[B]q = 10[/B]
Substituting q = 10 into Equation (1), we get:
n = 10 + 15
[B]n = 25[/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!

2 Asset Portfolio

Given a portfolio with 2 assets, this determines the expected return (mean), variance, and volatility (standard deviation) of the portfolio.

2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than

2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than twice a number of home runs the second player hit. how many home runs did each player hit?
Declare variables:
Let the first players home runs be a
Let the second players home runs be b
We're given two equations:
[LIST=1]
[*]a = 2b + 3
[*]a + b = 60
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for a:
2b + 3 + b = 60
Using our math engine, we [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B3%2Bb%3D60&pl=Solve']type this equation[/URL] in and get:
b = [B]19
[/B]
To solve for a, we substitute b = 19 into equation (1):
a = 2(19) + 3
a = 38 + 3
a = [B]41[/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 numbers that are equal have a sum of 60

2 numbers that are equal have a sum of 60
Let's choose 2 arbitrary variables for the 2 numbers
x, y
Were given 2 equations:
[LIST=1]
[*]x = y <-- Because we have the phrase [I]that are equal[/I]
[*]x + y = 60
[/LIST]
Because x = y in equation (1), we can substitute equation (1) into equation (2) for x:
y + y = 60
Add like terms to get:
2y = 60
Divide each side by 2:
2y/2 = 60/2
Cancel the 2's and we get:
y = [B]30
[/B]
Since x = y, x = y = 30
x = [B]30[/B]

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 minus 4 times another number is 6. The sum of 2 numbers is 8. Find the 2 numbers

2 times a number minus 4 times another number is 6. The sum of 2 numbers is 8. Find the 2 numbers.
Let the first number be x, and the second number be y. We're given two equations:
[LIST=1]
[*]2x - 4y = 6
[*]x + y = 8
[/LIST]
Using our simultaneous equation calculator, there are 3 ways to solve this:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+4y+%3D+6&term2=x+%2B+y+%3D+8&pl=Substitution']Substitution[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+4y+%3D+6&term2=x+%2B+y+%3D+8&pl=Elimination']Elimination[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+4y+%3D+6&term2=x+%2B+y+%3D+8&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
They all give the same answers:
(x, y) = [B](6.3333333, 1.6666667)[/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]

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]

20% of a number is x. What is 100% of the number? Assume x>0.

20% of a number is x. What is 100% of the number? Assume x>0.
Let the number be n. We're given:
0.2n = x <-- Since 20% = 0.2
To find n, we multiply each side of the equation by 5:
5(0.2)n = 5x
n = [B]5x[/B]

250 students have iPhones. This is one third of the population. How many students are there in total

250 students have iPhones. This is one third of the population. How many students are there in total?
Let the population be p. We're given:
1/3p = 250
Cross multiply:
p = 250 * 3
p = [B]750[/B]

3 boys share 100 in the ratio 1:2:2. how much each boy will get?

3 boys share 100 in the ratio 1:2:2. how much each boy will get?
Given the ratio 1 : 2 : 2, calculate the expected number of items from a population of 100
A ratio of 1 : 2 : 2 means that for every of item A, we can expect 2 of item B and 2 of item c
Therefore, our total group is 1 + 2 + 2 = 5
[SIZE=5][B]Calculate Expected Number of Item A:[/B][/SIZE]
Expected Number of Item A = 1 x 100/5
Expected Number of Item A = 100/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=100&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item A = 20/1
Expected Number of Item A = [B]20[/B]
[SIZE=5][B]Calculate Expected Number of Item B:[/B][/SIZE]
Expected Number of Item B = 2 x 100/5
Expected Number of Item B = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item B = 40/1
Expected Number of Item B = [B]40[/B]
[SIZE=5][B]Calculate Expected Number of Item C:[/B][/SIZE]
Expected Number of Item C = 2 x 100/5
Expected Number of Item C = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item C = 40/1
Expected Number of Item C = [B]40[/B]
[B]Final Answer:[/B]
(A, B, C) =[B] (20, 40, 40)[/B] for 1:2:2 on 100 people

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

35 m/s for 40 s. how far does it travel?

35 m/s for 40 s. how far does it travel?
This is a distance problem. The formula to relate, distance, rate, and time is:
d = rt
We are given r = 35 m/s and t = 40s. We want d
d = 35 m/s * 40s
d = [B]1,400 meters[/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]

4 adults and 3 children cost $40. Two adults and 6 children cost $38

4 adults and 3 children cost $40. Two adults and 6 children cost $38
Givens and Assumptions:
[LIST]
[*]Let the number of adults be a
[*]Let the number of children be c
[*]Cost = Price * Quantity
[/LIST]
We're given 2 equations:
[LIST=1]
[*]4a + 3c = 40
[*]2a + 6c = 38
[/LIST]
We can solve this system of equations 3 ways
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4a+%2B+3c+%3D+40&term2=2a+%2B+6c+%3D+38&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4a+%2B+3c+%3D+40&term2=2a+%2B+6c+%3D+38&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4a+%2B+3c+%3D+40&term2=2a+%2B+6c+%3D+38&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we use, we get:
[LIST]
[*][B]a = 7[/B]
[*][B]c = 4[/B]
[/LIST]

401(k) Balance

Determines your 401(k) balance given a salary history per year, contribution percentage rate, employer match percentage, and a rate of return.

414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost wa

414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost was $755.25. How many adults and children used the pool
Let the number of children who used the pool be c, and the number of adults who used the pool be a. We're given two equations:
[LIST=1]
[*]a + c = 414
[*]2a + 1.75c = 755.25
[/LIST]
We have a simultaneous equations. You can solve this any of 3 ways below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
Whichever method you choose, you get the same answer:
[LIST]
[*][B]a = 123[/B]
[*][B]c = 291[/B]
[/LIST]

45 water balloons were given to 9 children. If each child received the same number of water balloons

45 water balloons were given to 9 children. If each child received the same number of water balloons, how many water balloons did each child receive?
Water Balloons per child = Total Water Balloons / Number of Children
Water Balloons per child = 45/9
Water Balloons per child = [B]5[/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]

5 books and 5 bags cost $175. What is the cost of 2 books and 2 bags

5 books and 5 bags cost $175. What is the cost of 2 books and 2 bags
Let the cost of each book be b and the cost of each bag be c. We're given
5b + 5c = 175
We can factor this as:
5(b + c) = 175
Divide each side of the equation by 5, we get:
(b + c) = 35
The problem asks for 2b + 2c
Factor out 2:
2(b + c)
we know from above that (b + c) = 35, so we substitute:
2(35)
[B]70[/B]

5 Card Poker Hand

Calculates and details probabilities of the 10 different types of poker hands given 1 player and 1 deck of cards.

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]

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]

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]

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]

9 rulers cost the same as 11 erasers. One eraser cost 0.09 cents. What is the cost of 1 ruler

9 rulers cost the same as 11 erasers. One eraser cost 0.09 cents. What is the cost of 1 ruler
Let the cost of a ruler be r. We're given:
9r = 11(0.09)
9r = 0.99
Divide each side by 9 and we get:
r = [B]0.11[/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]

9 workers were hired to harvest potatoes from a field. each is given a plot which is 11*7 feet in si

9 workers were hired to harvest potatoes from a field. each is given a plot which is 11*7 feet in size. what is the total area of the field
The area of each plot is 11*7 = 77
With 9 workers, the total area of the field is:
9 * 77 = [B]693 sq feet[/B]

963 animals on a farm, 159 sheep and 406 cows and pigs. How many are pigs?

963 animals on a farm, 159 sheep and 406 cows and pigs. How many are pigs?
Set up equation to represent the total animals on the farm
Total Animals = Cows + Pigs + Sheep
Now plug in what is given
963 = 406 + Pigs + 159
Simplify:
Pigs + 565 = 963
Subtract 565 from each side
[B]Pigs = 398[/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 $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation

A $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by y = 654,000 ? 1800x dollars. After how many months will the value of the building be $409,200?
We want to know x for the equation:
654000 - 1800x = 409200
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=654000-1800x%3D409200&pl=Solve']type it in our math engine[/URL] and we get:
x = [B]136 months[/B]

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and short response questions are worth 8 points each. Write a system of linear equations that represents this situation
Assumptions:
[LIST]
[*]Let m be the number of multiple choice questions
[*]Let s be the number of short response questions
[/LIST]
Since total points = points per problem * number of problems, we're given 2 equations:
[LIST=1]
[*][B]m + s = 20[/B]
[*][B]3m + 8s = 100[/B]
[/LIST]
We can solve this system of equations 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[B]m = 12, s = 8[/B]

A 15 feet piece of string is cut into two pieces so that the longer piece is 3 feet longer than twic

A 15 feet piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
If the shorter piece is x, the longer piece is 20 - x
We also are given
15 - x = 2x + 3
Add x to each side:
3x + 3 = 15
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B3%3D15&pl=Solve']equation calculator[/URL], we get a shorter piece of:
[B]x = 4[/B]
The longer piece is:
15 - x
15 - 4
[B]11[/B]

A 20 feet piece of string is cut into two pieces so that the longer piece is 5 feet longer than twic

A 20 feet piece of string is cut into two pieces so that the longer piece is 5 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
If the shorter piece is x, the longer piece is 20 - x
We also are given
20 - x = 2x + 5
Add x to each side:
3x + 5 = 20
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B5%3D20&pl=Solve']equation calculator[/URL], we get a shorter piece of:
[B]x = 5
[/B]
The longer piece is:
20 - x
20 - 5
[B]15[/B]

A 3 gallon bottle of bleach cost $16.32. What is the price per cup?

A 3 gallon bottle of bleach cost $16.32. What is the price per cup?
We're given 16.32 / 3 gallons
Divide the top and bottom of the fraction by 3 to get the cost per gallon:
16.32/3 = 5.44 gallon
Using our [URL='https://www.mathcelebrity.com/liqm.php?quant=1&pl=Calculate&type=gallon']measurement converter[/URL], we see that:
1 gallon = 16 cups
So 5.44 /16 cups=[B]$0.34 per cup[/B]

A 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the ot

A 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the other. How long should the pieces be?
The key phrase in this problem is [B]two pieces[/B].
Declare Variables:
[LIST]
[*]Let the short piece length be s
[*]Let the long piece length be l
[/LIST]
We're given the following
[LIST=1]
[*]s = l - 10
[*]s + l = 98 (Because the two pieces add up to 98)
[/LIST]
Substitute equation (1) into equation (2) for s:
l - 10+ l = 98
Group like terms:
2l - 10 = 98
Solve for [I]l[/I] in the equation 2l - 10 = 98
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants -10 and 98. To do that, we add 10 to both sides
2l - 10 + 10 = 98 + 10
[SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE]
2l = 108
[SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE]
2l/2 = 108/2
l = [B]54[/B]
To solve for s, we substitute l = 54 into equation (1):
s = 54 - 10
s = [B]44[/B]
Check our work:
The shorter piece is 10 inches shorter than the longer piece since 54 - 44 = 10
Second check: Do both pieces add up to 98
54 + 44 ? 98
98 = 98

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 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 baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many m

a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many more tickets would they need to sell to earn at least $441?
Let the number of tickets above 42 be t.
A few things to note on this question:
[LIST]
[*]The phrase [I]at least[/I] means greater than or equal to, so we have an inequality.
[*]Earnings = Price * Quantity
[/LIST]
We're given:
Earnings = 4.50 * 42 + 4.5t >= 441
Earnings = 189 + 4.5t >= 441
We want to solve this inequality for t:
Solve for [I]t[/I] in the inequality 189 + 4.5t ? 441
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 189 and 441. To do that, we subtract 189 from both sides
4.5t + 189 - 189 ? 441 - 189
[SIZE=5][B]Step 2: Cancel 189 on the left side:[/B][/SIZE]
4.5t ? 252
[SIZE=5][B]Step 3: Divide each side of the inequality by 4.5[/B][/SIZE]
4.5t/4.5 ? 252.4.5
[B]t ? 56[/B]

A binomial probability experient is conducted with the given parameters. Compute the probability of

A binomial probability experient is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 40, p = 0.05, x = 2
P(2) =
Answer is [B]0.2777[/B]. Using Excel formula of =BINOMDIST(2,40,0.05,FALSE) or using our [URL='http://www.mathcelebrity.combinomial.php?n=+40&p=0.05&k=2&t=+5&pl=P%28X+%3D+k%29']binomial probability calculator[/URL]

A boat can carry 582 passengers to the base of a waterfall. A total of 13,105 people ride the boat t

A boat can carry 582 passengers to the base of a waterfall. A total of 13,105 people ride the boat today. All the rides are full except for the first ride. How many rides are given?
582 passengers on the boat
Let r be the number of rides
So we want to find r when:
582r = 13105
To solve for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=582r%3D13105&pl=Solve']type this equation into our math engine[/URL] and we get:
r = 22.517
If we round this down, setting 0.517 rides as the first ride, we get:
r = [B]22
[MEDIA=youtube]0J2YRPzKsoU[/MEDIA][/B]

a boat traveled 336 km downstream with the current. The trip downstream took 12 hours. write an equa

a boat traveled 336 km downstream with the current. The trip downstream took 12 hours. write an equation to describe this relationship
We know the distance (d) equation in terms of rate (r) and time (t) as:
d = rt
We're given d = 336km and t = 12 hours, so we have:
[B]336 km = 12t [/B] <-- this is our equation
Divide each side by 12 to solve for t:
12t/12 = 336/12
t = [B]28 km / hour[/B]

A boat traveled at a constant speed for 32 hours, covering a total distance of 597 kilometers. To th

A boat traveled at a constant speed for 32 hours, covering a total distance of 597 kilometers. To the nearest hundredth of a kilometer per hour, how fast was it going?
Distance = Rate * Time
We're given t = 32, and d = 597. Using our [URL='https://www.mathcelebrity.com/drt.php?d=+597&r=+&t=32&pl=Calculate+the+missing+Item+from+D%3DRT']distance, rate, and time calculator[/URL], we get:
r = [B]18.656 km/hr[/B]

A Bouquet of lillies and tulips has 12 flowers. Lillies cost $3 each, and tulips cost $2 each. The b

A Bouquet of lillies and tulips has 12 flowers. Lillies cost $3 each, and tulips cost $2 each. The bouquet costs $32. Write and solve a system of linear equations to find the number of lillies and tulips in the bouquet.
Let l be the number of lillies and t be the number of tulips. We're given 2 equations:
[LIST=1]
[*]l + t = 12
[*]3l + 2t = 32
[/LIST]
With this system of equations, we can solve it 3 ways.
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[LIST]
[*][B]l = 8[/B]
[*][B]t = 4[/B]
[/LIST]
[B]Now Check Your Work For Equation 1[/B]
l + t = 12
8 + 4 ? 12
12 = 12
[B]Now Check Your Work For Equation 2[/B]
3l + 2t = 32
3(8) + 2(4) ? 32
24 + 8 ? 32
32 = 32

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 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 car travels 71 feet each second.How many feet does it travel in 12 seconds?

A car travels 71 feet each second.How many feet does it travel in 12 seconds?
Distance = Rate * Time
We're given a rate of 71 feet per second and a time of 12 seconds. So we plug this in:
Distance = 71 feet/second * 12 seconds
[URL='https://www.mathcelebrity.com/drt.php?d=+&r=71&t=+12&pl=Calculate+the+missing+Item+from+D%3DRT']Distance[/URL] = [B]852 feet[/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 cash prize of $4600 is to be awarded at a fundraiser. if 2300 tickets are sold at $7 each, find th

a cash prize of $4600 is to be awarded at a fundraiser. if 2300 tickets are sold at $7 each, find the expected value.
Expected Value E(x) is:
E(x) = Probability of winning * Winning Price - Probability of losing * Ticket Price
[U]Since only 1 cash price will be given, 2299 will be losers:[/U]
E(x) = 4600 * (1/2300) - 2299/2300 * 7
E(x) = 2 - 0.99956521739 * 7
E(x) - 2 - 7
E(x) = [B]-5[/B]

A cash register contains $5 bills and $20 bills with a total value of $180 . If there are 15 bills t

A cash register contains $5 bills and $20 bills with a total value of $180 . If there are 15 bills total, then how many of each does the register contain?
Let f be the number of $5 dollar bills and t be the number of $20 bills. We're given the following equations:
[LIST=1]
[*]f + t = 15
[*]5f + 20t = 180
[/LIST]
We can solve this system of equations 3 ways. We get [B]t = 7[/B] and [B]f = 8[/B].
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]

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 cashier has a total of 52 bills in her cash drawer. There are only $10 bills and $5 bills in her

A cashier has a total of 52 bills in her cash drawer. There are only $10 bills and $5 bills in her drawer. The value of the bills is $320. How many $10 bills are in the drawer?
Let f be the amount of $5 bills in her drawer. Let t be the amount of $10 bills in her drawer. We're given two equations:
[LIST=1]
[*]f + t = 52
[*]5f + 10t = 320
[/LIST]
We have a system of equations. We can solve this 3 ways below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+52&term2=5f+%2B+10t+%3D+320&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+52&term2=5f+%2B+10t+%3D+320&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+52&term2=5f+%2B+10t+%3D+320&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter what method we choose, we get:
f = 40 and t = 12
So the answer for how many $10 bills are in the drawer is [B]12[/B].
Let's check our work for equation 1:
40 + 12 ? 52
52 = 52 <-- Confirmed
Let's check our work for equation 2:
5(40) + 10(12) ? 320
200 + 120 ? 320
320 = 320 <-- Confirmed

A child's bedroom is rectangular in shape with dimensions 17 feet by 15 feet. How many feet of wallp

A child's bedroom is rectangular in shape with dimensions 17 feet by 15 feet. How many feet of wallpaper border are needed to wrap around the entire room?
A rectangle has an Perimeter (P) of:
P = 2l + 2w
We're given l = 17 and w = 15. So we have:
P = 2(17) + 2(15)
P = 34 + 30
P = [B]64[/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 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 cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8

A cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8 1/4 cups, how much flour and how much sugar would it be?
Let f be the number of cups of sugar. And let f be the number of cups of flour. We're given two equations:
[LIST=1]
[*]f = 10s
[*]s + f = 8 & 1/4
[/LIST]
Substitute (1) into (2):
s + 10s = 8 & 1/4
11fs= 33/4 <-- 8 & 1/4 = 33/4
Cross multiply:
44s = 33
Divide each side by 44:
s= 33/44
Divide top and bottom by 11 and we get s [B]= 3/4 or 0.75[/B]
Now substitute this into (1):
f = 10(33/44)
[B]f = 330/44 or 7 & 22/44 or 7.5[/B]

A crate contains 300 coins and stamps. The coins cost $3 each and the stamps cost $1.5 each. The tot

A crate contains 300 coins and stamps. The coins cost $3 each and the stamps cost $1.5 each. The total value of the items is $825. How many coins are there?
Let c be the number of coins, and s be the number of stamps. We're given:
[LIST=1]
[*]c + s = 300
[*]3c + 1.5s = 825
[/LIST]
We have a set of simultaneous equations, or a system of equations. We can solve this 3 ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]
No matter which way we pick, we get:
s = 50
c = [B]250[/B]

A cube has an edge that is x cm long. What is the capacity of C(x)?

A cube has an edge that is x cm long. What is the capacity of C(x)?
Capacity is another word for volume, or the amount an object will hold. Given a side x, the capacity (volume) of a cube is:
C(x) = [B]x^3[/B]

A culture of bacteria doubles every hour. If there are 500 bacteria at the beginning, how many bacte

A culture of bacteria doubles every hour. If there are 500 bacteria at the beginning, how many bacteria will there be after 9 hours?
Assumptions and givens;
[LIST]
[*]h is the number of hours.
[*]B(h) is the number of bacteria at time h
[*]B(0) is the starting bacteria amount
[*]Doubling means multiplying by 2, so we have:
[/LIST]
B(h) = B(0) * 2^h
We want h = 9, so we have:
B(9) = 500 * 2^9
B(9) = 500 * 512
B(9) = [B]256,000[/B]

A dog and a cat together cost $100. If the price of the dogs $90 more than the cat, what is the cost

A dog and a cat together cost $100. If the price of the dogs $90 more than the cat, what is the cost of the cat?
Set up givens and equations
[LIST]
[*]Let the cost of the dog be d
[*]Let the cost of the cat be c
[/LIST]
We're given 2 equations:
[LIST=1]
[*]c + d = 100
[*]d = c + 90
[/LIST]
Substitute equation (2) into equation (1) for d
c + c + 90 = 100
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=c%2Bc%2B90%3D100&pl=Solve']math engine[/URL], we see that:
c = [B]5
[/B]
Substitute c = 5 into equation (2) above:
d = 5 + 90
d = [B]95[/B]

A fair coin is tossed 4 times. a) How many outcomes are there in the sample space? b) What is the pr

A fair coin is tossed 4 times.
a) How many outcomes are there in the sample space?
b) What is the probability that the third toss is heads, given that the first toss is heads?
c) Let A be the event that the first toss is heads, and B be the event that the third toss is heads. Are A
and B independent? Why or why not?
a) 2^4 = [B]16[/B] on our [URL='http://www.mathcelebrity.comcointoss.php?hts=+HTHTHH&hct=+2&tct=+1&fct=+5>=no+more+than&nmnl=+2&htpick=heads&tossct=+4&calc=5&montect=+500&pl=Calculate+Probability']coin toss calculator[/URL]
b) On the link above, 4 of those outcomes have H and H in toss 1 and 3. So it's [B]1/4 or 0.25[/B]
c) [B]Yes, each toss is independent of each other.[/B]

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 29. F

A first number plus twice a second number is 10. Twice the first number plus the second totals 29. Find the numbers.
Let the first number be x. Let the second number be y. We are given the following two equations:
[LIST=1]
[*]x + 2y = 10
[*]2x + y = 29
[/LIST]
We can solve this 3 ways using:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Substitution']Substitution[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Elimination']Elimination[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
Using any of the 3 methods, we get the same answers of [B](x, y) = (16, -3)[/B]

A first number plus twice a second number is 11. Twice the first number plus the second totals 34. F

A first number plus twice a second number is 11. Twice the first number plus the second totals 34. Find the numbers.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]x + 2y = 11
[*]2x + y = 34
[/LIST]
Using our simultaneous equations calculator, we have 3 methods to solve this:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
All 3 methods give the same solution:
[LIST]
[*][B]x = 19[/B]
[*][B]y = -4[/B]
[/LIST]

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 22. Twice the first number plus the second totals 28. F

A first number plus twice a second number is 22. Twice the first number plus the second totals 28. Find the numbers.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x + 2y = 22 <-- Since twice means multiply by 2
[*]2x + y = 28 <-- Since twice means multiply by 2
[/LIST]
We have a set of simultaneous equations. We can solve this three ways
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28+&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*][B]x = 11 & 1/3[/B]
[*][B]y = 5 & 1/3[/B]
[/LIST]

A first number plus twice a second number is 3. Twice the first number plus the second totals 24.

A first number plus twice a second number is 3. Twice the first number plus the second totals 24.
Let the first number be x. Let the second number be y. We're given:
[LIST=1]
[*]x + 2y = 3 <-- Because [I]twice[/I] means multiply by 2
[*]2x + y = 24 <-- Because [I]twice[/I] means multiply by 2
[/LIST]
We have a system of equations. We can solve it any one of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which way we choose, we get:
[LIST]
[*]x = [B]15[/B]
[*]y = [B]-6[/B]
[/LIST]

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 first number plus twice a second number is 7

A first number plus twice a second number is 7
Let the first number be x. Let the second number be y. We're given:
[LIST]
[*]A first number is x
[*]A second number is y
[*]Twice the second number means we multiply y by 2: 2y
[*][I]Plus [/I]means we add x to 2y: x + 2y
[*]The phrase [I]is[/I] means an equation, so we set x + 2y equal to 7
[/LIST]
[B]x + 2y = 7[/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 fraction has a value of 3/4. If 7 is added to the numerator, the resulting fraction is equal to th

A fraction has a value of 3/4. If 7 is added to the numerator, the resulting fraction is equal to the reciprocal of the original fraction. Find the original fraction.
Let the fraction be x/y. We're given two equations:
[LIST=1]
[*]x/y = 3/4
[*](x + 7)/y = 4/3. [I](The reciprocal of 3/4 is found by 1/(3/4)[/I]
[/LIST]
Cross multiply equation 1 and equation 2:
[LIST=1]
[*]4x = 3y
[*]3(x + 7) = 4y
[/LIST]
Simplifying, we get:
[LIST=1]
[*]4x = 3y
[*]3x + 21 = 4y
[/LIST]
If we divide equation 1 by 4, we get:
[LIST=1]
[*]x = 3y/4
[*]3x + 21 = 4y
[/LIST]
Substitute equation (1) into equation (2) for x:
3(3y/4) + 21 = 4y
9y/4 + 21 = 4y
Multiply the equation by 4 on both sides to eliminate the denominator:
9y + 84 = 16y
To solve this equation for y, we type it in our math engine and we get:
y = [B]12
[/B]
We then substitute y = 12 into equation 1 above:
x = 3 * 12/4
x = 36/4
x = [B]9
[/B]
So our original fraction x/y = [B]9/12[/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 gardener wants to fence a circular garden of diameter 21cm. Find the length of the rope he needs t

A gardener wants to fence a circular garden of diameter 21cm. Find the length of the rope he needs to purchase, if he makes 2round of fence Also find the cost of the rope, if it costs Rs4 per meter (take pie as 22/7)
Circumference of a circle = Pi(d).
Given Pi = 22/7 for this problem, we have:
C = 22/7(21)
C = 22*3
[B]C = 66[/B]

A gasoline tank is leaking at a rate of n gallons in t hours. If the gasoline cost $2 per gallon, wh

A gasoline tank is leaking at a rate of n gallons in t hours. If the gasoline cost $2 per gallon, what is the value of the gasoline that will be lost in m minutes?
n gallons / t hours = n/t gallons per hour are leaking
The value of the gas that leaks each hour is $2, so we have:
2n/t dollar per hour is leaking
Value per minute means we divide by 60:
2n/60t
Dividing top and bottom by 2 to simplify, we have:
n/30t
Given m minutes, we multiply to get:
[B]nm/30t[/B]

A girl is pedaling her bicycle at a velocity of 0.10 km/hr. How far will she travel in two hours?

A girl is pedaling her bicycle at a velocity of 0.10 km/hr. How far will she travel in two hours?
The distance formula is:
d = rt
We're given a rate (r) of 0.10km/hr
We're given time (t) of 2 hours
Plug these values into the distance formula and we get:
d= 0.1 * 2
d = [B]0.2km
[MEDIA=youtube]w80E_YM-tDA[/MEDIA][/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 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 is 2 years older than b who is twice as old as c. if the total ages of a,b and c is 42, then how o

a is 2 years older than b who is twice as old as c. if the total ages of a,b and c is 42, then how old is b
We're given 3 equations:
[LIST=1]
[*]a = b + 2
[*]b = 2c
[*]a + b + c = 42
[/LIST]
Substituting equation (2) into equation (1), we have:
a = 2c + 2
Since b = 2c, we substitute both of these into equation (3) to get:
2c + 2 + 2c + c = 42
To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=2c%2B2%2B2c%2Bc%3D42&pl=Solve']type this equation into our math engine[/URL] and we get:
c = 8
Now take c = 8 and substitute it into equation (2) above:
b = 2(8)
b = [B]16[/B]

A jet travels 832 km in 5 hours. At this rate, how far could the jet fly in 12 hours? What is the ra

A jet travels 832 km in 5 hours. At this rate, how far could the jet fly in 12 hours? What is the rate of speed of the jet?
Distance = rate * time. We're given D = 832 and t = 5. Using our [URL='https://www.mathcelebrity.com/drt.php?d=+832&r=+&t=+5&pl=Calculate+the+missing+Item+from+D%3DRT']drt calculator[/URL], we solve or rate to get:
[B]r = 166.4[/B]
The problems asks for a distance D when t = 12 hours and r = 166.4 from above. Using our [URL='https://www.mathcelebrity.com/drt.php?d=&r=+166.4&t=+12&pl=Calculate+the+missing+Item+from+D%3DRT']drt calculator solving for d[/URL], we get:
d = [B]1,996.8 km[/B]

A jet travels at 485 miles per hour. Which equation represents the distance, d, that the jet will tr

A jet travels at 485 miles per hour. Which equation represents the distance, d, that the jet will travel in t hours.
The distance formula is:
d = rt
We're given r = 485, so we have:
[B]d = 485t[/B]

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall,

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall, how high up the wall does the ladder reach?
We have a right triangle, where the ladder is the hypotenuse, and we want the measurement of one leg.
Set up the pythagorean theorem with these given items using our P[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=7&hypinput=25&pl=Solve+Missing+Side']ythagorean Theorem Calculator[/URL].
We get Side 1 = [B]24 feet.[/B]

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 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 has a slope of 7 and a y-intercept of -4. What is its equation in slope intercept form

A line has a slope of 7 and a y-intercept of -4. What is its equation in slope intercept form
The slope-intercept equation for a line:
y = mx + b where m is the slope
Given m = 7, we have:
y = 7x + b
The y-intercept is found by setting x to 0:
y = 7(0) + b
y = 0 + b
y = b
We're given the y-intercept is -4, so we have:
b = -4
So our slope-intercept equation is:
[B]y = 7x - 4[/B]

A line in the xy-plane passes through the origin and has a slope of 4/5. What points lie on that lin

A line in the xy-plane passes through the origin and has a slope of 4/5. What points lie on that line.
Our line equation is:
y = mx + b
We're given:
m = 4/5
(x, y) = (0, 0)
So we have:
0 = 4/5(0) + b
0 = 0 + b
b = 0
Therefore, our line equation is:
y = 4/5x
[URL='https://www.mathcelebrity.com/function-calculator.php?num=y%3D4%2F5x&pl=Calculate']Start plugging in values here to get a list of points[/URL]

A machine prints 230 movie posters each hour. Write and solve an equation to find the number of hour

A machine prints 230 movie posters each hour. Write and solve an equation to find the number of hours it takes the machine to print 1265 posters.
Let h be the number of hours. We're given the following expression for the printing output of the machine:
230h
The questions asks for how long (h) to print 1265 posters, so we setup the equation:
230h = 1265
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=230h%3D1265&pl=Solve']type this equation into our math engine[/URL] and we get:
h = [B]5.5 hours[/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 purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket?
Declare variables:
[LIST]
[*]Let a be the number of adult's tickets
[*]Let c be the number of children's tickets
[/LIST]
Cost = Price * Quantity
We're given two equations:
[LIST=1]
[*]a + c = 20
[*]15a + 10c = 225
[/LIST]
Rearrange equation (1) in terms of a:
[LIST=1]
[*]a = 20 - c
[*]15a + 10c = 225
[/LIST]
Now that I have equation (1) in terms of a, we can substitute into equation (2) for a:
15(20 - c) + 10c = 225
Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225
We first need to simplify the expression removing parentheses
Simplify 15(20 - c): Distribute the 15 to each term in (20-c)
15 * 20 = (15 * 20) = 300
15 * -c = (15 * -1)c = -15c
Our Total expanded term is 300-15c
Our updated term to work with is 300 - 15c + 10c = 225
We first need to simplify the expression removing parentheses
Our updated term to work with is 300 - 15c + 10c = 225
[SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE]
(-15 + 10)c = -5c
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
-5c + 300 = + 225
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 300 and 225. To do that, we subtract 300 from both sides
-5c + 300 - 300 = 225 - 300
[SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE]
-5c = -75
[SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE]
-5c/-5 = -75/-5
c = [B]15[/B]
Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a:
a = 20 - 15
a = [B]5[/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 movie theater charges $7 for adults and $3 for seniors on a particular day when 324 people paid an

A movie theater charges $7 for adults and $3 for seniors on a particular day when 324 people paid an admission the total receipts were 1228 how many were seniors and how many were adults?
Let the number of adult tickets be a. Let the number of senior tickets be s. We're given two equations:
[LIST=1]
[*]a + s = 324
[*]7a + 3s = 1228
[/LIST]
We have a set of simultaneous equations we can solve using 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]a = 64[/B]
[*][B]s = 260[/B]
[/LIST]

A movie theater charges 7.00 for adults and 2.00 for seniors citizens. On a day when 304 people paid

A movie theater charges 7.00 for adults and 2.00 for seniors citizens. On a day when 304 people paid for admission, the total receipt were 1118. How many who paid were adults ? How many were senior citizens?
Let a be the number of adult tickets. Let s be the number of senior citizen tickets. We're given two equations:
[LIST=1]
[*]a + s = 304
[*]7a + 2s = 1118
[/LIST]
We can solve this system of equations three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Cramers+Method']Cramer's Method[/URL]
[/LIST]
No matter which way we choose, we end up with the same answer:
[LIST]
[*]a = [B]102[/B]
[*]s = [B]202[/B]
[/LIST]

A new car worth $30,000 is depreciating in value by $3,000 per year. After how many years will the c

A new car worth $30,000 is depreciating in value by $3,000 per year. After how many years will the cars value be $9,000
Step 1, the question asks for Book Value. Let y be the number of years since purchase.
We setup an equation B(y) which is the Book Value at time y.
B(y) = Sale Price - Depreciation Amount * y
We're given Sale price = $30,000, depreciation amount = 3,000, and B(y) = 9000
30000 - 3000y = 9000
To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=30000-3000y%3D9000&pl=Solve']type this in our math engine[/URL] and we get:
y = [B]7
[/B]
To check our work, substitute y = 7 into B(y)
B(7) = 30000 - 3000(7)
B(7) = 30000 - 21000
B(7) = 9000
[MEDIA=youtube]oCpBBS7fRYs[/MEDIA]

a paper boy delivers thirteen paper to an apartment complex. if these deliveries compose one-seventh

a paper boy delivers thirteen paper to an apartment complex. if these deliveries compose one-seventh of his route, how many papers does he deliver
Let d be the total number of deliveries the paper boy makes on the route.
d
We're given, d/7 = 13
d = 13 * 7
d = [B]91
[MEDIA=youtube]HRviz-3fn5c[/MEDIA][/B]

A parabola has a Vertex at (4,-2) and a Focus at (6,-2). Find the equation of the parabola

A parabola has a Vertex at (4,-2) and a Focus at (6,-2). Find the equation of the parabola and the lotus rectum.
Equation of a parabola given the vertex and focus is:
([I]x[/I] – [I]h[/I])^2 = 4[I]p[/I]([I]y[/I] – [I]k[/I])
The vertex (h, k) is 4, -2
The distance is p, and since the y coordinates of -2 are equal, the distance is 6 - 4 = 2.
So p = 2
Our parabola equation becomes:
(x - 4)^2 = 4(2)(y - -2)
[B](x - 4)^2 = 8(y + 2)[/B]
Latus rectum of a parabola is 4p, where p is the distance between the vertex and the focus
LR = 4p
LR = 4(2)
[B]LR = 8[/B]

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. Wh

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. What is the length of each of the other two sides?
A parallelogram is a rectangle bent on it's side. So we have the perimeter formula P below:
P = 2l + 2w
We're given w = 17 and P = 54. So we plug this into the formula for perimeter:
2l + 2(17) = 54
2l + 34 = 54
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B34%3D54&pl=Solve']equation calculator[/URL], we get [B]l = 10[/B].

A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables

A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables is $37. The total cost to rent 2 chairs and 6 tables is $64. What is the cost to rent each chair and each table?
Let c be the cost of renting one chair and t be the cost of renting one table. We're given two equations:
[LIST=1]
[*]5c + 3t = 37
[*]2c + 6t =64
[/LIST]
We have a system of equations. Using our system of equations calculator, we can solve this problem any of 3 ways below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5c+%2B+3t+%3D+37&term2=2c+%2B+6t+%3D+64&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5c+%2B+3t+%3D+37&term2=2c+%2B+6t+%3D+64&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5c+%2B+3t+%3D+37&term2=2c+%2B+6t+%3D+64&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
All 3 methods give the same answer:
[LIST]
[*][B]Chairs (c) cost $1.25[/B]
[*][B]Tables (t) cost $10.25[/B]
[/LIST]

A person has $13,000 invested in stock A and stock B. Stock A currently sells for $20 a share and

A person has $13,000 invested in stock A and stock B. Stock A currently sells for $20 a share and stock B sells for $90 a share. If stock B triples in value and stock A goes up 50%, his stock will be worth $33,000. How many shares of each stock does he own?
Set up the given equations, where A is the number of shares for Stock A, and B is the number of shares for Stock B
[LIST=1]
[*]90A + 20B = 13000
[*]3(90A) + 1.5(20B) = 33000 <-- [I]Triple means multiply by 3, and 50% gain means multiply by 1.5[/I]
[/LIST]
Rewrite (2) by multiplying through:
270A + 30B = 33000
Using our simultaneous equations calculator, we get [B]A = 100 and B = 200[/B]. Click the links below to solve using each method:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]
Check our work using equation (1)
90(100) + 20(200) ? 13,000
9000 + 4000 ? 13,000
13000 = 13000

A person invested 30,000 in stocks and bonds. Her investment in bonds is 2000 more than 1-third her

A person invested 30,000 in stocks and bonds. Her investment in bonds is 2000 more than 1-third her investments in stocks. How much did she invest in stocks? How much did she invest in bonds?
Let the stock investment be s, and the bond investment be b. We're given:
[LIST=1]
[*]b + s = 30000
[*]b = 1/3s + 2000
[/LIST]
Plug in (2) to (1):
1/3s + 2000 + s = 30000
Group like terms:
(1/3 + 1)s + 2000 = 30000
Since 1 = 3/3, we have:
4/3s + 2000 = 30000
Subtract 2000 from each side:
4/3s + 2000 - 2000 = 30000 - 2000
Cancel the 2000's on the left side, we get:
4/3s = 28000
[URL='https://www.mathcelebrity.com/1unk.php?num=4%2F3s%3D28000&pl=Solve']Typing this equation into our calculator[/URL], we get:
s = [B]21,000[/B]

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuou

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV = Pe^{rt} V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years.
Substituting our given numbers in where P = 96,300, r = 0.028, and t = 7, we get:
V = 96,300 * e^(0.028 * 7)
V = 96,300 * e^0.196
V = 96,300 * 1.21652690533
V = [B]$117,151.54[/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 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 professor wants to test all possible pairwise comparisons among three means. If we need to maintai

A professor wants to test all possible pairwise comparisons among three means. If we need to maintain an experiment-wise alpha of 0.05, what is the error rate per comparison after applying Bonferroni correction?
We are given:
[LIST]
[*]? = 0.05
[*]n = 3
[/LIST]
Bonferroni Correction = ?/n
Bonferroni Correction = 0.05/3
Bonferroni Correction = [B]0.01666666667[/B]

A quarter of the learners in a class have blond hair and two thirds have brown hair. The rest of the

A quarter of the learners in a class have blond hair and two thirds have brown hair. The rest of the learners in the class have black hair. How many learners in the class if 9 of them have blonde hair?
Total learners = Blond + Brown + Black
Total Learners = 1/4 + 2/3 + Black
Total Learners will be 1, the sum of all fractions
1/4 + 2/3 + Black = 1
Using common denominators of 12, we have:
3/12 + 8/12 + Black = 12/12
11/12 + Black = 12/12
Subtract 11/12 from each side:
Black = 1/12
Let t be the total number of people in class. We are given for blondes:
1/4t = 9
Multiply each side by 4
[B]t = 36[/B]
Brown Hair
2/3(36) = 24
Black Hair
1/12(36) = 3

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 rectangle has a length of x-7 and a width of x + 5. Write an expression that represents the area o

a rectangle has a length of x-7 and a width of x + 5. Write an expression that represents the area of the rectangle in terms of x.
Area of a rectangle (A) with length(l) and width (w) is expressed as follows:
A = lw
Plugging in our values given above, we have:
[B]A = (x - 7)(x + 5)[/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 has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?
We know the rectangle has the following formulas:
Area = lw
Perimeter = 2l + 2w
Given an area of 238 and a perimeter of 62, we have:
[LIST=1]
[*]lw = 238
[*]2(l + w) = 62
[/LIST]
Divide each side of (1) by w:
l = 238/w
Substitute this into (2):
2(238/w + w) = 62
Divide each side by 2:
238/w + w = 31
Multiply each side by w:
238w/w + w^2 = 31w
Simplify:
238 + w^2 = 31w
Subtract 31w from each side:
w^2 - 31w + 238 = 0
We have a quadratic. So we run this through our [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2-31w%2B238%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL] and we get:
w = (14, 17)
We take the lower amount as our width and the higher amount as our length:
[B]w = 14
l = 17
[/B]
Check our work for Area:
14(17) = 238 <-- Check
Check our work for Perimeter:
2(17 + 14) ? 62
2(31) ? 62
62 = 62 <-- Check

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 field is twice as long as it is wide. If the perimeter is 360 what are the dimensions?

A rectangular field is twice as long as it is wide. If the perimeter is 360 what are the dimensions?
We are given or know the following about the rectangle
[LIST]
[*]l = 2w
[*]P = 2l + 2w
[*]Since P = 360, we have 2l + 2w = 360
[/LIST]
Since l = 2w, we have 2l + (l) = 360
3l = 360
Divide by 3, we get [B]l = 120[/B]
Which means w = 120/2
[B]w = 60[/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
Given l = length and w = width, The perimeter of a rectangle is 2l + 2w, 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 math engine[/URL] and we get:
w = [B]7
[/B]
To solve for l, we substitute w = 7 into equation (1):
l = 3(7)
l = [B]21[/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 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 repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and s

A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and solve an equation to find the number of hours of labor spent repairing the car
Set up the cost equation C(h) where h is the number of labor hours:
C(h) = Labor Cost per hour * h + Parts Cost
We're given C(h) = 553, Parts Cost = 265, and Labor Cost per Hour = 48. So we plug these in:
48h + 265 = 553
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=48h%2B265%3D553&pl=Solve']type it in our math engine[/URL] and we get:
h = [B]6 hours[/B]

A restaurant is open for 10 ˝ hours during the day. The restaurant has 5 ˝ families coming and leavi

A restaurant is open for 10 ˝ hours during the day. The restaurant has 5 ˝ families coming and leaving every hour. A family has 4 members. How many people have visited the restaurant during the day?
[U]Given:[/U]
[LIST]
[*]10 & 1/2 = 10.5 hours
[*]5 & 1/2 = 5.5 families
[/LIST]
Total Visitors = Hours Open * Families per hour * member per family
Total Visitors = 10.5 * 5.5 * 4
Total Visitors = [B]231[/B]

A school wants to buy a chalkboard that measures 1 yard by 2 yards. The chalkboard costs $27.31 per

A school wants to buy a chalkboard that measures 1 yard by 2 yards. The chalkboard costs $27.31 per square yard. How much will the chalkboard cost?
Area of a chalkboard is denoted as :
A = lw
Given 1 yard width and 2 years length of the chalkboard, we have:
A = 2(1)
A = 2 square yards
Therefore, total cost is:
Total Cost = $27.31 * square yards
Total Cost = $27.31(2)
Total Cost = [B]$54.62[/B]

A set of 19 scores has a mean of 6.3. A new score of 8 is then included in the data set. What is th

A set of 19 scores has a mean of 6.3. A new score of 8 is then included in the data set. What is the new mean?
We know the mean formula is:
Sum of scores / Number of Scores = Mean
We're given mean = 6.3 and number of scores = 19, so we have:
Sum of scores / 19 = 6.3
Cross multiply:
Sum of scores = 19 * 6.3
Sum of scores = 119.7
Now a new score is added of 8, so we have:
Sum of scores = 119.7 + 8 = 127.7
Number of scores = 19 + 1 = 20
So our new mean is:
Mean = Sum of scores / Number of Scores
Mean = 127.7/20
Mean = [B]6.385[/B]
[COLOR=rgb(0, 0, 0)][SIZE=5][FONT=arial][B][/B][/FONT][/SIZE][/COLOR]

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 shopkeeper buys a box of 20 cans of cola for $10. He sells the cans for 65 cents each. Work out hi

A shopkeeper buys a box of 20 cans of cola for $10. He sells the cans for 65 cents each. Work out his percentage profit.
[U]Calculate Revenue[/U]
Revenue = Sale price per can * number of cans
Revenue = 0.65 * 20
Revenue = 13
[U]Calculate Profit given a cost of $10:[/U]
Profit = Revenue - Cost
Profit = 13 - 10
Profit = 3
[U]Calculate Percentage Profit:[/U]
Percentage Profit = Profit/Revenue * 100%
Percentage Profit = 3/13 * 100%
Percentage Profit = 0.23076923076 * 100%
Percentage Profit = [B]23.08%[/B]

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.
Declare variables:
[LIST]
[*]Let f be the father's age
[*]Let s be the son's age
[/LIST]
We're given two equations:
[LIST=1]
[*]s = f/4
[*]f - s = 30. [I]The reason why we subtract s from f is the father is older[/I]
[/LIST]
Using substitution, we substitute equaiton (1) into equation (2) for s:
f - f/4 = 30
To remove the denominator/fraction, we multiply both sides of the equation by 4:
4f - 4f/4 = 30 *4
4f - f = 120
3f = 120
To solve for f, we divide each side of the equation by 3:
3f/3 = 120/3
Cancel the 3's on the left side and we get:
f = [B]40[/B]

A spherical water tank holds 11,500ft^3 of water. What is the diameter?

A spherical water tank holds 11,500ft^3 of water. What is the diameter?
The tank holding amount is volume. And the volume of a sphere is:
V = (4pir^3)/3
We know that radius is 1/2 of diameter:
r =d/2
So we rewrite our volume function:
V = 4/3(pi(d/2)^3)
We're given V = 11,500 so we have:
4/3(pi(d/2)^3) = 11500
Multiply each side by 3/4
4/3(3/4)(pi(d/2)^3) = 11,500*3/4
Simplify:
pi(d/2)^3 = 8625
Since pi = 3.1415926359, we divide each side by pi:
(d/2)^3 = 8625/3.1415926359
(d/2)^3 = 2745.42
Take the cube root of each side:
d/2 = 14.0224
Multiply through by 2:
[B]d = 28.005[/B]

A square has a perimeter of 24 inches. What is the area of the square?

A square has a perimeter of 24 inches. What is the area of the square?
Perimeter of a square = 4s where s = the length of a side. Therefore, we have:
4s = P
4s = 24
Using our equation solver, [URL='https://www.mathcelebrity.com/1unk.php?num=4s%3D24&pl=Solve']we type in 4s = 24[/URL] and get:
s = 6
The problems asks for area of a square. It's given by
A = s^2
Plugging in s = 6, we get:
A = 6^2
A = 6 * 6
A = [B]36
[/B]
Now if you want a shortcut in the future, type in the shape and measurement you know. Such as:
[I][URL='https://www.mathcelebrity.com/square.php?num=24&pl=Perimeter&type=perimeter&show_All=1']square perimeter = 24[/URL][/I]
From the link, you'll learn every other measurement about the square.

A stack of lumber is 8 feet wide, 5 feet high, and 2 feet long. Give the volume of the stack

A stack of lumber is 8 feet wide, 5 feet high, and 2 feet long. Give the volume of the stack
The lumber stack is a rectangular solid. The Volume V is found from the length (l), width (w), and height (h) by:
V = lwh
Plugging in our given values, we get:
V = 2 * 8 * 5
V = [B]80 cubic feet[/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 submarine is 75 feet below sea level. It descends another 25 feet every 10 seconds for 3 minutes.

A submarine is 75 feet below sea level. It descends another 25 feet every 10 seconds for 3 minutes. What integer represents the submarines current location?
Assumptions and givens:
[LIST]
[*]Let m be the number of minutes
[*]10 seconds is 1/6 of a minute, 6 (10) seconds blocks per minute * 3 minutes = 18 (10 second blocks)
[*]Below sea level is a negative number
[/LIST]
[U]Current depth:[/U]
-25(18) - 75
-450 - 75
[B]-525[/B]

A survey of 950 college students found that 85% of the men and 90% of the women identified math as t

A survey of 950 college students found that 85% of the men and 90% of the women identified math as their favorite subject. If altogether 834 students reported math to be their favorite subject how many men and women participated in the survey
Let m be the number of men and w be the number of women. We are given 2 equations
[LIST=1]
[*]m + w = 950
[*]0.85m + 0.90w = 834
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+w+%3D+950&term2=0.85m+%2B+0.90w+%3D+834&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[LIST]
[*]m = [B]420[/B]
[*]w = [B]530[/B]
[/LIST]

A survey was given to 120 6th grade students at middle school. It showed the 42 students said they l

A survey was given to 120 6th grade students at middle school. It showed the 42 students said they like playing at the park. What % of the students said they like playing there?
We want [I][URL='https://www.mathcelebrity.com/perc.php?num=42&den=120&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']42 is what percent of 120[/URL][/I]
Using our calculator above, we get [B]35%[/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 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 assumed that the average of grades for a math test was 80. Imagine 20 students took the te

A teacher assumed that the average of grades for a math test was 80. Imagine 20 students took the test and the 95% confidence interval of grades was (83, 90). Can you reject the teacher's assumption?
a. Yes
b. No
c. We cannot tell from the given information
[B]a. Yes[/B]
[I]At the 0.05 significance level, yes since 80 is not in the confidence interval.[/I]

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 test has twenty questions worth 100 points total. the test consists of true/false questions worth

A test has twenty questions worth 100 points total. the test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each. How many true/false questions are on the test?
Let m be the number of multiple choice questions and t be the number of true/false questions. We're given:
[LIST=1]
[*]m + t = 20
[*]11m + 3t = 100
[/LIST]
We can solve this system of equations 3 ways below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the following answers:
[LIST]
[*][B]m = 5[/B]
[*][B]t = 15[/B]
[/LIST]
Check our work in equation 1:
5 + 15 ? 20
[I]20 = 20[/I]
Check our work in equation 2:
11(5) + 3(15) ? 100
55 + 45 ? 100
[I]100 = 100[/I]

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 poin

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
Let the number of true/false questions be t. Let the number of multiple choice questions be m. We're given two equations:
[LIST=1]
[*]m + t = 20
[*]11m + 3t = 100
[/LIST]
We have a set of simultaneous equations. We can solve this using 3 methods:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we pick, we get the same answer:
[LIST]
[*][B]m = 5[/B]
[*][B]t = 15[/B]
[/LIST]

A text message plan costs $7 per month plus $0.28 per text. Find the monthly cost for x text message

A text message plan costs $7 per month plus $0.28 per text. Find the monthly cost for x text messages.
We set up the cost function C(x) where x is the number of text messages per month:
C(x) = Cost per text * x + Monthly cost
Plugging in our given numbers, we get:
[B]C(x) = 0.28x + 7[/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 tortoise is walking in the desert. It walks at a speed of 5 meters per minute for 12.5 meters. For

A tortoise is walking in the desert. It walks at a speed of 5 meters per minute for 12.5 meters. For how many minutes does it walk?
Distance formula (d) for a rate (r) and time (t) is:
d = rt
We're given d = 12.5 and r = 5
12.5 = 5t
5t = 12.5
Solve for t. Divide each side of the equation by 5:
5t/5 = 12.5/5
Cancel the 5's on left side and we get:
t = [B]2.5[/B]

A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selec

A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will be between 85 and 125 points?
For x = 125, our z-score and probability is seen [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+125&mean=+105&stdev=+20&n=+1&pl=P%28X+%3C+Z%29']here[/URL]
Z = 1
P(x < 1) = 0.841345
For x = 85, our z-score and probability is seen [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+85&mean=+105&stdev=+20&n=+1&pl=P%28X+%3C+Z%29']here[/URL]
Z = -1
P(x < -1) = 0.158655
So what we want is the probability between these values:

0.841345 - 0.158655 = [B]0.68269[/B]

0.841345 - 0.158655 = [B]0.68269[/B]

A used book store also started selling used CDs and videos. In the first week, the store sold a comb

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold
Let c be the number of CDs sold, and v be the number of videos sold. We're given 2 equations:
[LIST=1]
[*]c + v = 40
[*]4c + 6v = 180
[/LIST]
You can solve this system of equations three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter what method we choose, we get [B]c = 30, v = 10[/B].
Now let's check our work for both given equations for c = 30 and v = 10:
[LIST=1]
[*]30 + 10 = 40 <-- This checks out
[*]4c + 6v = 180 --> 4(30) + 6(10) --> 120 + 60 = 180 <-- This checks out
[/LIST]

A used book store also started selling used CDs and videos. In the first week, the store sold a comb

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold.
Let the number of cd's be c and number of videos be v. We're given two equations:
[LIST=1]
[*]c + v = 40
[*]4c + 6v = 180
[/LIST]
We can solve this system of equations using 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[B]c = 30
v = 10[/B]

a varies inversely with b, c and d

a varies inversely with b, c and d
Varies inversely means we divide. Given a constant, k, we have:
[B]a = k/bcd[/B]

A washer and a dryer cost 600 combined. The cost of the washer is 3 times the cost of the dryer. Wha

A washer and a dryer cost 600 combined. The cost of the washer is 3 times the cost of the dryer. What is the cost of the dryer?
Let w be the cost of the washer. Let d be the cost of the dryer. We have 2 given equations:
[LIST=1]
[*]w + d = 600
[*]w = 3d
[/LIST]
Substitute (2) into (1)
(3d) + d = 600
4d = 600
[URL='http://www.mathcelebrity.com/1unk.php?num=4d%3D600&pl=Solve']Run it through our equation calculator[/URL], to get [B]d = 150[/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 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]

According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eatin

According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24. Over your lifetime, how many years will you spend on each of these activities?
Assumptions:
[LIST]
[*]Let years eating be e
[*]Let years sleeping be s
[/LIST]
We're given:
[LIST=1]
[*]s = e + 24
[*]e + s = 32
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for s:
e + e + 24 = 32
To solve this equation for e, we [URL='https://www.mathcelebrity.com/1unk.php?num=e%2Be%2B24%3D32&pl=Solve']type it in our math engine[/URL] and we get:
e = [B]4
[/B]
Now, we take e = 4 and substitute it into equation (1) to solve for s:
s = 4 + 24
s = [B]28[/B]

Accounting Rate of Return

Given an initial investment and a set of returns, this calculates the Accounting Rate of Return

Accuracy and Precision

Given an integer or decimal, this determines the precision and accuracy (scale)

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]

Affine Cipher

Builds the Affine Cipher Translation Algorithm from a string given an a and b value

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]

Ahmad has a jar containing only 5-cent and 20-cent coins. In total there are 31 coins with a total v

Ahmad has a jar containing only 5-cent and 20-cent coins. In total there are 31 coins with a total value of $3.50. How many of each type of coin does Ahmad have?
Let the number of 5-cent coins be f.
Let the number of 20-cent coins be t.
We're given two equations:
[LIST=1]
[*]f + t = 31
[*]0.05f + 0.2t = 3.50
[/LIST]
We can solve this simultaneous system of equations 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[LIST]
[*][B]f = 18[/B]
[*][B]t = 13[/B]
[/LIST]

Alberto and Willie each improved their yards by planting daylilies and ivy. They bought their suppli

Alberto and Willie each improved their yards by planting daylilies and ivy. They bought their supplies from the same store. Alberto spent $64 on 3 daylilies and 8 pots of ivy. Willie spent $107 on 9 daylilies and 7 pots of ivy. What is the cost of one daylily and the cost of one pot of ivy?
Assumptions:
[LIST]
[*]Let d be the cost of one daylily
[*]Let i be the cost of one pot of ivy
[/LIST]
Givens:
[LIST=1]
[*]3d + 8i = 64
[*]9d + 7i = 107
[/LIST]
To solve this system of equations, you can use any of three methods below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3d+%2B+8i+%3D+64&term2=9d+%2B+7i+%3D+107&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3d+%2B+8i+%3D+64&term2=9d+%2B+7i+%3D+107&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3d+%2B+8i+%3D+64&term2=9d+%2B+7i+%3D+107&pl=Cramers+Method']Cramer's Method[/URL]
[/LIST]
No matter what method we use, we get the same answer:
[LIST]
[*][B]d = 8[/B]
[*][B]i = 5[/B]
[/LIST]
[B][MEDIA=youtube]K1n3niERg-U[/MEDIA][/B]

Alexandra was given a gift card for a coffee shop. Each morning, Alexandra uses the card to buy one

Alexandra was given a gift card for a coffee shop. Each morning, Alexandra uses the card to buy one cup of coffee. The original amount of money on the gift card was $45 and each cup of coffee costs $2.50. Write an equation for A(x),A(x), representing the amount money remaining on the card after buying xx cups of coffee.
We start with 45, and each cup of coffee decreases our balance by 2.50, so we subtract:
[B]A(x) = 45 - 2.50x[/B]

Algebra Master (Polynomials)

Given 2 polynomials this does the following:

1) Polynomial Addition

2) Polynomial Subtraction

Also generates binomial theorem expansions and polynomial expansions with or without an outside constant multiplier.

1) Polynomial Addition

2) Polynomial Subtraction

Also generates binomial theorem expansions and polynomial expansions with or without an outside constant multiplier.

Algebraic Substitutions

Given an algebraic statement with variables [a-z], this calculator takes a set of given substitution values, i.e., x=2,y=3,z=4, and evaluates your statement using the substitution values.

Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the siste

Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara?
Let a be Alice's age, b be Barbara's age, and c be Carol's age. We have 3 given equations:
[LIST=1]
[*]a = b - 3
[*]b = c - 5
[*]a + b + c = 68
[/LIST]
Rearrange (2)
c = b + 5
Now plug in (1) and (2) revised into (3). We want to isolate for b.
a + b + c = 68
(b - 3) + b + (b + 5) = 68
Combine like terms:
(b + b + b) + (5 - 3) = 68
3b + 2 = 68
Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=3b%2B2%3D68&pl=Solve']equation calculator[/URL], and we get b = [B]22[/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 had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil co

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

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]

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]

An airplane is flying at 38,800 feet above sea level. The airplane starts to descend at a rate of 18

An airplane is flying at 38,800 feet above sea level. The airplane starts to descend at a rate of 1800 feet per minute. Let m be the number of minutes. Which of the following expressions describe the height of the airplane after any given number of minutes?
Let m be the number of minutes. Since a descent equals a [U]drop[/U] in altitude, we subtract this in our Altitude function A(m):
[B]A(m) = 38,800 - 1800m[/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 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 operation is defined by a*b=3a-b.Calculate the exact value of 2*3

An operation is defined by a*b=3a-b.Calculate the exact value of 2*3
We're given a = 2 and b = 3. So the operator says:
3(2) - 3
6 - 3
[B]3[/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

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]

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 is 11, which is 3 years younger than 4 times her sister's age.

Angie is 11, which is 3 years younger than 4 times her sister's age.
Let her sister's age be a. We're given the following equation:
4a - 3 = 11
To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=4a-3%3D11&pl=Solve']type this equation into our math engine[/URL] and we get:
[B]a = 3.5[/B]

Angle Ratio for a Triangle

Given an angle ratio for a triangle of a:b:c, this determines the angle measurements of the triangle.

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]

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]

Assume that in your Abnormal Psychology class you have earned test scores of 74%, 78%, and 63%, and

Assume that in your Abnormal Psychology class you have earned test scores of 74%, 78%, and 63%, and only one test remains. If you need a mean score of 80% to earn a B for you final grade, is it possible for you to accomplish this? Assume there is no extra credit. Show work and explain why or why not. Hint: you're taking 4 tests total.
Using our [URL='https://www.mathcelebrity.com/missingaverage.php?num=74%2C78%2C63&avg=80&pl=Calculate+Missing+Score']missing average calculator with our 3 given scores and target average[/URL], we get:
A 4th score needed of 105.
Since the most you can score on an exam is 100, [B][I]this is impossible[/I][/B].

Assume that you make random guesses for 5 true-or-false questions

Assume that you make random guesses for 5 true-or-false questions.
(a) What is the probability that you get all 5 answers correct? (Show work and write the answer in simplest fraction form)
(b) What is the probability of getting the correct answer in the 5th question, given that the first four answers are all wrong? (Show work and write the answer in simplest fraction form)
(c) If event A is “Getting the correct answer in the 5th question” and event B is “The first four answers are all wrong”. Are event A and event B independent? Please explain.
(a) Correct Answer on each one is 1/2 or 0.5. Since all are independent events, we have:
(1/2)^5 = [B]1/32[/B]
(b) We have [B]1/2[/B]
(1/2)^4 * 1/2/((1/2)^4)
c) [B]Independent since you could have gotten correct or wrong on any of the 4 and the probability does not change[/B]

at a bakery the cost of one cupcake and 2 slices of pie is $12.40. the cost of 2 cupcakes and 3 slic

at a bakery the cost of one cupcake and 2 slices of pie is $12.40. the cost of 2 cupcakes and 3 slices of pie costs $20.20. what is the cost of one cupcake?
Let the number of cupcakes be c
Let the number of pie slices be p
Total Cost = Unit cost * quantity
So we're given two equations:
[LIST=1]
[*]1c + 2p = 12.40
[*]2c + 3p = 20.20
[/LIST]
We can solve this system of equations any one of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]c = 3.2[/B]
[*]p = 4.6
[/LIST]

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 certain university, 60% of the students enrolled in a math course, 50% are enrolled in an Engli

At a certain university, 60% of the students enrolled in a math course, 50% are enrolled in an English course, and 40% are enrolled in both. What percentage of the students are enrolled in an English course and/or a math course?
Let M be a math course, E be an english course, We are given:
[LIST]
[*]P(M) = 0.6
[*]P(E) = 0.5
[*]P(E AND M) = 0.4
[*]We want P(E U M)
[/LIST]
Using [URL='http://www.mathcelebrity.com/probunion2.php?pa=0.6+&pb=+0.5&paintb=+0.4&aub=+&pl=Calculate']two event probability[/URL], we get [B]P(E U M) = 0.7[/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 football game, a vender sold a combined total of 117 sodas and hot dogs. The number of hot dogs

At a football game, a vender sold a combined total of 117 sodas and hot dogs. The number of hot dogs sold was 59 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
[U]Let h = number of hot dogs and s = number of sodas. Set up our given equations:[/U]
[LIST=1]
[*]h + s = 117
[*]h = s - 59
[/LIST]
[U]Substitute (2) into (1)[/U]
(s - 59) + s = 117
[U]Combine s terms[/U]
2s - 59 = 117
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2s-59%3D117&pl=Solve']equation solver[/URL], we find:[/U]
[B]s = 88
[/B]
[U]Plug s = 88 into (2)[/U]
h = 88 - 59
[B]h = 29[/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 the end of the 2021 NBA season, the NY Knicks had 10 more wins than losses. This NBA season the N

At the end of the 2021 NBA season, the NY Knicks had 10 more wins than losses. This NBA season the NY Knicks played a total of 72 times. Find a solution to this problem and explain.
Let w be the number of wins
Let l be the number of losses
We're given two equations:
[LIST=1]
[*]w = l + 10
[*]l + w = 72
[/LIST]
To solve this system of equations, substitute equation (1) into equation (2) for w:
l + l + 10 = 72
To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l%2Bl%2B10%3D72&pl=Solve']type it in our math engine[/URL] and we get:
l = [B]31
[/B]
To solve for w, we substitute l = 31 into equation (1):
w = 31 + 10
w = [B]41[/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]

Ava is 4 times as old as Peter. What equation can be used to find Peter’s age?

Ava is 4 times as old as Peter. What equation can be used to find Peter’s age?
[U]Assumptions[/U]
Let a be Ava's age
Let p be Peter's age
We're given:
a = 4p
To find Peter's age, we divide each side of the equation by 4 to get:
a/4 = 4p/4
p = [B]a/4[/B]

Balance Sheet

Given various asset and liability entries, this determines various calculations that can be made from the balance sheet.

Balance with Interest

Calculates the final account balance given a beginning balance, interest rate, and interest crediting period.

Balancing Equations

Given 4 numbers, this will use the four operations: addition, subtraction, multiplication, or division to balance the equations if possible.

Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants co

Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants cost $4 each. If she plans to spend at least $20 and purchase less than 15 plants in total, create a system of equations or inequalities that model the situation. Define the variables you use.
[U]Define variables[/U]
[LIST]
[*]Let c be the number of corn plants
[*]Let p be the number of potato plants
[/LIST]
Since cost = price * quantity, we're given two inequalities:
[LIST=1]
[*][B]3p + 4c >= 20 (the phrase [I]at least[/I] means greater than or equal to)[/B]
[*][B]c + p < 15[/B]
[/LIST]

Basal Metabolic Rate (BMR)

Given a gender, an age, and a height/weight in inches/pounds or meters/kilograms, this will calculate the Basal Metabolic Rate (BMR)

Basic m x n Matrix Operations

Given 2 matrices |A| and |B|, this performs the following basic matrix operations

* Matrix Addition |A| + |B|

* Matrix Subtraction |A| - |B|

* Matrix Multiplication |A| x |B|

* Scalar multiplication rA where r is a constant.

* Matrix Addition |A| + |B|

* Matrix Subtraction |A| - |B|

* Matrix Multiplication |A| x |B|

* Scalar multiplication rA where r is a constant.

Basic Math Operations

Given 2 numbers, this performs the following arithmetic operations:

* Addition (Adding) (+)

* Subtraction (Subtracting) (-)

* Multiplication (Multiplying) (x)

* Long division (Dividing) with a remainder (÷)

* Long division to decimal places (÷)

* Partial Sums (Shortcut Sums)

* Short Division

* Duplication and Mediation

* Addition (Adding) (+)

* Subtraction (Subtracting) (-)

* Multiplication (Multiplying) (x)

* Long division (Dividing) with a remainder (÷)

* Long division to decimal places (÷)

* Partial Sums (Shortcut Sums)

* Short Division

* Duplication and Mediation

Basic Statistics

Given a number set, and an optional probability set, this calculates the following statistical items:

Expected Value

Mean = μ

Variance = σ^{2}

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Expected Value

Mean = μ

Variance = σ

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Bayes Rule

Calculates the conditional probabilities of (B given A) of 2 events and a conditional probability event using Bayes Rule

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 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]

Bernoulli Trials

Given a success probability p and a number of trials (n), this will simulate Bernoulli Trials and offer analysis using the Bernoulli Distribution. Also calculates the skewness, kurtosis, and entropy

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.

Better Buy Comparison

Given two items with a price and quantity, this determines which is the better buy by comparing unit prices. Finds the better deal.

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 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]

Bond Price Formulas

Given a face value, coupon percent, yield percent, term, and redemption value, this calculates the price of a bond using the four price formulas for bonds

1) Basic

2) Premium/Discount

3) Base

4) Makeham

1) Basic

2) Premium/Discount

3) Base

4) Makeham

Braille Translator

Given a phrase with letters, numbers, and most punctuation symbols, the calculator will perform the following duties:

1) Translate that phrase to Braille

2) Calculate the number of dots in the message

3) Calculate the number of empty spaces in the message

1) Translate that phrase to Braille

2) Calculate the number of dots in the message

3) Calculate the number of empty spaces in the message

Break Even

Given a fixed cost, variable cost, and revenue function or value, this calculates the break-even point

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]

calculate cos(x) given tan(x)=8/15

calculate cos(x) given tan(x)=8/15
tan(x) = sin(x)/cos(x)
sin(x)/cos(x) = 8/15
Cross multiply:
15sin(x) = 8cos(x)
Divide each side by 8
[B]cos(x) = 15sin(x)/8[/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]

Cameron knows that 2 dogs are given 8 cups of food and 3 dogs are given 12 cups of food. How much fo

Cameron knows that 2 dogs are given 8 cups of food and 3 dogs are given 12 cups of food. How much food will be given to 5 dogs?
2:8 --> 3:12 --> 1:4
This means for every dog, 4 cups of food are given. With 5 dogs, we have:
5 * 4 = [B]20 cups of food[/B]

Capitalized Cost and Periodic Charge

Given an Asset Value (A), a Salvage Value (S) at time (N), a sinking fund rate of (j), an effective rate of interest (i), and maintenance expense (M), this calculator solves for periodic charge (H) and capitalized cost (K)

Carmen is serving her child french fries and chicken wings for lunch today. Let f be the number of f

Carmen is serving her child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Carmen wants the total calorie count from the french fries and chicken wings to be less than 500 calories. Using the values and variables given, write an inequality describing this.
We have:
25f + 100c < 50
Note: We use < and not <= because it states less than in the problem.

Cars and trucks are the most popular vehicles. last year, the number of cars sold was 39,000 more th

Cars and trucks are the most popular vehicles. last year, the number of cars sold was 39,000 more than 3 times the number of trucks sold. There were 216,000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year.
Let c be the number of cars.
Let t be the number of trucks.
We're given two equations:
[LIST=1]
[*]c = 3t + 39000
[*]c + t = 216000
[/LIST]
Substitute equation (1) into equation (2) for c:
3t + 39000 + t = 216000
To solve this equation for t, [URL='https://www.mathcelebrity.com/1unk.php?num=3t%2B39000%2Bt%3D216000&pl=Solve']we type it in our math engine [/URL]and we get:
t = [B]44,250[/B]

Cartesian Product

Given a Set A and Set B, this calculates the Cartesian Product A × B

Cevian Triangle Relations

Given a triangle with a cevian, this will solve for the cevian or segments or sides based on inputs

Chain Discounts and Net Cost Price and Net Cost Equivalent

Given a chain discount and an original price, this calculates the total discount and net cost price.

Chang is serving his child french fries and chicken wings for lunch today. Let f be the number of f

Chang is serving his child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Chang wants the total calorie count from the french fries and chicken wings to be less than 600 calories. Using the values and variables given, write an inequality describing this.
We have [B]25f + 100c < 600[/B] as our inequality.

Chebyshevs Theorem

Using Chebyshevs Theorem, this calculates the following:

Probability that random variable X is within k standard deviations of the mean.

How many k standard deviations within the mean given a P(X) value.

Probability that random variable X is within k standard deviations of the mean.

How many k standard deviations within the mean given a P(X) value.

Chi-Square Critical Values

Given a probability, this calculates the critical value for the right-tailed and left-tailed tests for the Chi-Square Distribution. CHIINV from Excel is used as well.

Chinese Remainder Theorem

Given a set of modulo equations in the form:

x ≡ a mod b

x ≡ c mod d

x ≡ e mod f

the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.

Given that the n_{i} portions are not pairwise coprime and you entered two modulo equations, then the calculator will attempt to solve using the Method of Successive Subsitution

x ≡ a mod b

x ≡ c mod d

x ≡ e mod f

the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.

Given that the n

Choose the equation of a line in standard form that satisfies the given conditions. perpendicular to

Choose the equation of a line in standard form that satisfies the given conditions. perpendicular to 4x + y = 8 through (4, 3).
Step 1: Find the slope of the line 4x + y = 8.
In y = mx + b form, we have y = -4x + 8.
The slope is -4.
To be perpendicular to a line, the slope must be a negative reciprocal of the line it intersects with.
Reciprocal of -4 = -1/4
Negative of this = -1(-1/4) = 1/4
Using our [URL='https://www.mathcelebrity.com/slope.php?xone=4&yone=3&slope=+0.25&xtwo=3&ytwo=2&bvalue=+&pl=You+entered+1+point+and+the+slope']slope calculator[/URL], we get [B]y = 1/4x + 2[/B]

Circle Equation

This calculates the standard equation of a circle and general equation of a circle from the following given items:

* A center (h,k) and a radius r

* A diameter A(a_{1},a_{2}) and B(b_{1},b_{2})

This also allows you to enter a standard or general form equation so that the center (h,k) and radius r can be determined.

* A center (h,k) and a radius r

* A diameter A(a

This also allows you to enter a standard or general form equation so that the center (h,k) and radius r can be determined.

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.

Coin Combinations

Given a selection of coins and an amount, this determines the least amount of coins needed to reach that total.

Coin Values

This calculates the total value of a given amount of:

* Pennies

* Nickels

* Dimes

* Quarters

* Half-Dollars

* Dollars

* Pennies

* Nickels

* Dimes

* Quarters

* Half-Dollars

* Dollars

Combination with Variable

Calculates the following:

Solves for r given n and the combination value.

Solves for n given r and the combination value

Solves for r given n and the combination value.

Solves for n given r and the combination value

Combined Ratio

Given a ratio a:b and a ratio b:c, this determines the combined ratio a:c

Compare Raises

Given two people with a salary and annual raise amount, this determines how long it takes for the person with the lower salary to catch the person with the higher salary.

Complementary and Supplementary Angles

This calculator determines the complementary and supplementary angle of a given angle that you enter OR it checks to see if two angles that you enter are complementary or supplementary.

Complex Number Operations

Given two numbers in complex number notation, this calculator:

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

Compound Interest Accumulated Balance

Given an interest rate per annum compounded annually (i), semi-annually, quarterly, monthly, semi-monthly, weekly, and daily, this calculates the accumulated balance after (n) periods

Compound Interest and Annuity Table

Given an interest rate (i), number of periods to display (n), and number of digits to round (r), this calculator produces a compound interest table. It shows the values for the following 4 compound interest annuity functions from time 1 to (n) rounded to (r) digits:

v^{n}

d

(1 + i)^{n}

a_{n|}

s_{n|}

ä_{n|i}

s_{n|i}

Force of Interest δ^{n}

v

d

(1 + i)

a

s

ä

s

Force of Interest δ

Confidence Interval for the Mean

Calculates a (90% - 99%) estimation of confidence interval for the mean given a small sample size using the student-t method with (n - 1) degrees of freedom or a large sample size using the normal distribution Z-score (z value) method including Standard Error of the Mean. confidence interval of the mean

Confidence Interval of a Proportion

Given N, n, and a confidence percentage, this will calculate the estimation of confidence interval for the population proportion π including the margin of error. confidence interval of the population proportion

Confidence Interval/Hypothesis Testing for the Difference of Means

Given two large or two small distriutions, this will determine a (90-99)% estimation of confidence interval for the difference of means for small or large sample populations.

Also performs hypothesis testing including standard error calculation.

Also performs hypothesis testing including standard error calculation.

Congruence Modulo n

Given a possible congruence relation a ≡ b (mod n), this determines if the relation holds true (b is congruent to c modulo n).

Connor runs 2 mi more each day than David. The sum of the distances they run each week is 56 mi. How

Connor runs 2 mi more each day than David. The sum of the distances they run each week is 56 mi. How far does David run each day?
Let Connor's distance be c
Let David's distance be d
We're given two equations:
[LIST=1]
[*]c = d + 2
[*]7(c + d) = 56
[/LIST]
Simplifying equation 2 by dividing each side by 7, we get:
[LIST=1]
[*]c = d + 2
[*]c + d = 8
[/LIST]
Substitute equation (1) into equation (2) for c
d + 2 + d = 8
To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=d%2B2%2Bd%3D8&pl=Solve']type this equation into our calculation engine[/URL] and we get:
d = [B]3[/B]

Consider a firm that has two assembly lines, 1 and 2, both producing calculator. Assume that you hav

Consider a firm that has two assembly lines, 1 and 2, both producing calculator. Assume that you have purchased a calculator and it turns out to be defective. And the line 1 produces 60% of all calculators produced.
L1: event that the calculator is produced on line 1
L2: event that the calculator is produced on line 2
Suppose that your are given the conditional information:
10% of the calculator produced on line 1 is defective
20% of the calculator produced on line 2 is defective
Q: If we choose one defective, what is the probability that the defective calculator comes from Line 1 and Line2?
L1 = event that the calculator is produced on line 1 = 0.6
L2 = event that the calculator is produced on line 2 = 1 - 0.6 = 0.4
D = Defective
D|L1 Defective from Line 1 = 0.1
D|L2 = Defective from Line 2 = 0.20
[U]Defective from Line 1[/U]
P(L1|D) = P(L1)P(D/L1) / [ P(L1)P(D/L1) + P(L2)P(D/L2)]
P(L1|D) = (.60)(.10) /[(.60)(.10)+ (.40)(.20)]
[B]P(L1|D) = 0.4286[/B]
[U]Defective from Line 2[/U]
P(L2|D) = P(L2)P(D/L2) / [ P(L1)P(D/L1) + P(L2)P(D/L2)]
P(L2|D) = (.40)(.20) /[(.60)(.10)+ (.40)(.20)]
[B]P(L2|D) = 0.5714[/B]

Consider the following 15 numbers 1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20 - The mean o

Consider the following 15 numbers
1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20
- The mean of the last 10 numbers is TWICE the mean of the first 10 numbers
- The sum of the last 2 numbers is FIVE times the sum of the first 3 numbers
(i) Calculate the values of x and y
We're given two equations:
[LIST=1]
[*](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10 = 2(1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/10
[*]3x - 20 = 5(1 + 2 + y - 4)
[/LIST]
Let's evaluate and simplify:
[LIST=1]
[*](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10 = (1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/5
[*]3x - 20 = 5(y - 1)
[/LIST]
Simplify some more:
[URL='https://www.mathcelebrity.com/polynomial.php?num=x%2B6%2B7%2B8%2By%2B9%2B10%2B12%2B3x%2B20&pl=Evaluate'](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10[/URL] = (4x + y + 72)/10
[URL='https://www.mathcelebrity.com/polynomial.php?num=1%2B2%2By-4%2B4%2B5%2Bx%2B6%2B7%2B8%2By&pl=Evaluate'](1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/5[/URL] = (2y + x + 29)/5
5(y - 1) = 5y - 5
So we're left with:
[LIST=1]
[*](4x + y + 72)/10 = (2y + x + 29)/5
[*]3x - 20 = 5y - 5
[/LIST]
Cross multiply equations in 1, we have:
5(4x + y + 72) = 10(2y + x + 29)
20x + 5y + 360 = 20y + 10x + 290
We have:
[LIST=1]
[*]20x + 5y + 360 = 20y + 10x + 290
[*]3x - 20 = 5y - 5
[/LIST]
Combining like terms:
[LIST=1]
[*]10x - 15y = -70
[*]3x - 5y = 15
[/LIST]
Now we have a system of equations which we can solve any of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
(x, y) = [B](-115, -72)[/B]

Construct a confidence interval of the population proportion at the given level of confidence. x = 1

Construct a confidence interval of the population proportion at the given level of confidence.
x = 120, n = 300, 99% confidence
Round to 3 decimal places as needed
[B]0.327 < p < 0.473[/B] using our [URL='http://www.mathcelebrity.com/propconf.php?bign=300&smalln=120&conf=99&pl=Proportion+Confidence+Interval']proportion confidence interval calculator[/URL]

Container Arrangements

Given a set of items inside a container, this calculates the probability that you draw certain items in the following fashion:

Draw__all__ the items

Draw__any of__ the items

How many ways can you choose m items of a, n items of b, o items of c, etc.

Draw

Draw

How many ways can you choose m items of a, n items of b, o items of c, etc.

Cost Recovery Method

Given a sales price, cost, and set of payments, this determines the gross profit per year based on the cost recovery method.

Cost Revenue Profit

Given a total cost, variable cost, revenue amount, and profit unit measurement, this calculates profit for each profit unit

Country A produces about 7 times the amount of diamonds in carats produce in Country B. If the total

Country A produces about 7 times the amount of diamonds in carats produce in Country B. If the total produced in both countries is 40,000,000 carats, find the amount produced in each country.
Set up our two given equations:
[LIST=1]
[*]A = 7B
[*]A + B = 40,000,000
[/LIST]
Substitute (1) into (2)
(7B) + B = 40,000,000
Combine like terms
8B = 40,000,000
Divide each side by 8
[B]B = 5,000,000[/B]
Substitute this into (1)
A = 7(5,000,000)
[B]A = 35,000,000[/B]

Coupon Comparison

Given a cost of goods, a dollar off coupon, and a percentage off coupon, this calculator will compare the two deals and determine which one is of more value. If the dollar coupon wins, the calculator will project the break even price where the dollar coupon would surpass the percentage coupon

Covariance and Correlation coefficient (r) and Least Squares Method and Exponential Fit

Given two distributions X and Y, this calculates the following:

* Covariance of X and Y denoted Cov(X,Y)

* The correlation coefficient r.

* Using the least squares method, this shows the least squares regression line (Linear Fit) and Confidence Intervals of α and Β (90% - 99%)

Exponential Fit

* Coefficient of Determination r squared r^{2}

* Spearmans rank correlation coefficient

* Wilcoxon Signed Rank test

* Covariance of X and Y denoted Cov(X,Y)

* The correlation coefficient r.

* Using the least squares method, this shows the least squares regression line (Linear Fit) and Confidence Intervals of α and Β (90% - 99%)

Exponential Fit

* Coefficient of Determination r squared r

* Spearmans rank correlation coefficient

* Wilcoxon Signed Rank test

Credit Card Balance

This calculator shows 3 methods for paying off a credit card balance on a monthly installment basis given an outstanding balance and an Annual Percentage Rate (APR):

1) Minimum Payment Amount

2) Minimum Percentage Amount

3) Payoff in Years

1) Minimum Payment Amount

2) Minimum Percentage Amount

3) Payoff in Years

Critical Z-values

Given a probability from a normal distribution, this will generate the z-score critical value. Uses the NORMSINV Excel function.

Cross Partitions

Given a set of partitions, this determines the cross partitions.

Cross Product

Given two vectors A and B in R^{3}, this calculates the cross product A × B as well as determine if the two vectors are parallel

Crypto Scams

I'd like to warn our fans about a crypto scam going around.
The site is [URL]https://crypto-fortress.com[/URL].
The scam runs like this...
[LIST]
[*]You're asked to deposit money, a minimum of $1,000 in BTC.
[*]You're given credits on the money from their mining/aribtrage plan.
[*]However, when it comes time to cash out after a week, they suddenly tell you, their is some magical agreement (which you never signed nor is on their website) where you now have to pay 25% of your profits to them and you'll get a withdrawal code for the rest.
[*]When you press them on how they pay 75% of your profits from a 25% deposit which makes no sense, they tell you that it's how things work.
[/LIST]

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 makes 9 dollars for each hour of work. Write an equation to represent his total pay p after work

Dan makes 9 dollars for each hour of work. Write an equation to represent his total pay p after working h hours.
We know that pay (p) on an hourly basis (h) equals:
p = Hourly Rate * h
We're given an hourly rate of 9, so we have:
p = [B]9h[/B]

Dan needs 309 programs for the school play on Thursday. How many boxes of programs will he need, giv

Dan needs 309 programs for the school play on Thursday. How many boxes of programs will he need, given that each box contains 41 programs?
Each box contains 41 programs, so we divide 309 programs by 41 programs per box to get our boxes:
309/41 using our [URL='https://www.mathcelebrity.com/longdiv.php?num1=309&num2=41&pl=Long%20Division%20%28Decimals%29']division calculator[/URL] is 7.5365.
Since we don't have fractional boxes, we round up to the next highest integer. [B]8 boxes[/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]

Density

Solves for any of the 3 items in the Density Formula, Density (D), Mass (M), and Volume (V) (Capacity), with 2 given items.

Determine the formula of the given statement by following the procedures. Choose any number then add

Determine the formula of the given statement by following the procedures. Choose any number then add 2. Multiply your answer to 3 and minus 2
For the phrase [I]choose any number[/I] we can use an arbitrary variable, let's call it x.
Add 2:
x + 2
Multiply your answer to 3:
3(x + 2)
And minus 2 which means we subtract:
[B]3(x + 2) - 2[/B]

Determine ux and sigma(x) from the given parameters of the population and sample size u = 76, sigma

Determine ux and sigma(x) from the given parameters of the population and sample size
u = 76, sigma = 28, n = 49
ux = ?
sigma(x) = ?
[B]u = ux = 76[/B]
sigma(x) = sigma/sqrt(n) so we have
28/sqrt(49) = 28/7 = [B]4[/B]

Determine whether the statement is true or false. If 0 < a < b, then Ln a < Ln b

Determine whether the statement is true or false. If 0 < a < b, then Ln a < Ln b
We have a logarithmic property that states:
ln(a) - ln(b) = ln (a / b)
We're given a < b, so (a / b) < 1
Therefore:
ln (a / b) < 0
And since ln(a) - ln(b) = ln (a / b)
Then Ln(a) - Ln(b) < 0
So this is [B]TRUE[/B]

Dewey Decimal System Classification

Given a 3 digit code, this will determine the class, division, and section of the library book using the Dewey Decimal System.

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time pe

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.
Our givens are:
[LIST]
[*]I = 450
[*]P = 3000
[*]t = 3
[*]We want r
[/LIST]
450 = 3000(r)(3)
450 = 9000r
Divide each side by 9000
[B]r = 0.05[/B]

difference between 2 positive numbers is 3 and the sum of their squares is 117

difference between 2 positive numbers is 3 and the sum of their squares is 117
Declare variables for each of the two numbers:
[LIST]
[*]Let the first variable be x
[*]Let the second variable be y
[/LIST]
We're given 2 equations:
[LIST=1]
[*]x - y = 3
[*]x^2 + y^2 = 117
[/LIST]
Rewrite equation (1) in terms of x by adding y to each side:
[LIST=1]
[*]x = y + 3
[*]x^2 + y^2 = 117
[/LIST]
Substitute equation (1) into equation (2) for x:
(y + 3)^2 + y^2 = 117
Evaluate and simplify:
y^2 + 3y + 3y + 9 + y^2 = 117
Combine like terms:
2y^2 + 6y + 9 = 117
Subtract 117 from each side:
2y^2 + 6y + 9 - 117 = 117 - 117
2y^2 + 6y - 108 = 0
This is a quadratic equation:
Solve the quadratic equation 2y2+6y-108 = 0
With the standard form of ax2 + bx + c, we have our a, b, and c values:
a = 2, b = 6, c = -108
Solve the quadratic equation 2y^2 + 6y - 108 = 0
The quadratic formula is denoted below:
y = -b ± sqrt(b^2 - 4ac)/2a
[U]Step 1 - calculate negative b:[/U]
-b = -(6)
-b = -6
[U]Step 2 - calculate the discriminant ?:[/U]
? = b2 - 4ac:
? = 62 - 4 x 2 x -108
? = 36 - -864
? = 900 <--- Discriminant
Since ? is greater than zero, we can expect two real and unequal roots.
[U]Step 3 - take the square root of the discriminant ?:[/U]
?? = ?(900)
?? = 30
[U]Step 4 - find numerator 1 which is -b + the square root of the Discriminant:[/U]
Numerator 1 = -b + ??
Numerator 1 = -6 + 30
Numerator 1 = 24
[U]Step 5 - find numerator 2 which is -b - the square root of the Discriminant:[/U]
Numerator 2 = -b - ??
Numerator 2 = -6 - 30
Numerator 2 = -36
[U]Step 6 - calculate your denominator which is 2a:[/U]
Denominator = 2 * a
Denominator = 2 * 2
Denominator = 4
[U]Step 7 - you have everything you need to solve. Find solutions:[/U]
Solution 1 = Numerator 1/Denominator
Solution 1 = 24/4
Solution 1 = 6
Solution 2 = Numerator 2/Denominator
Solution 2 = -36/4
Solution 2 = -9
[U]As a solution set, our answers would be:[/U]
(Solution 1, Solution 2) = (6, -9)
Since one of the solutions is not positive and the problem asks for 2 positive number, this problem has no solution

Digraph Items

Given a digraph, this determines the leader, and symmetric matrix.

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]

During a performance, a juggler tosses one ball straight upward while continuing to juggle three oth

During a performance, a juggler tosses one ball straight upward while continuing to juggle three others. The height f(t), in feet, of the ball is given by the polynomial function f(t) = ?16t^2 + 26t + 3, where t is the time in seconds since the ball was thrown. Find the height of the ball 1 second after it is tossed upward.
We want f(1):
f(1) = ?16(1)^2 + 26(1) + 3
f(1) = -16(1) + 26 + 3
f(1) = -16 + 26 + 3
f(1) = [B]13[/B]

During a recent season Miguel Cabrera and Mike Jacobs hit a combined total of 46 home runs. Cabrera

During a recent season Miguel Cabrera and Mike Jacobs hit a combined total of 46 home runs. Cabrera hit 6 more home runs than Jacobs how many home runs did each player hit
Let c be Miguel Cabrera's home runs and j be Mike Jacobs home runs. We are given two equations:
[LIST=1]
[*]c + j = 46
[*]c = j + 6
[/LIST]
Substitute (2) into (1)
(j + 6) + j = 46
Combine like terms:
2j + 6 = 46
[URL='https://www.mathcelebrity.com/1unk.php?num=2j%2B6%3D46&pl=Solve']Plugging this into our equation calculator[/URL], we get [B]j = 20[/B].
Substitute this into equation (2), we have:
c = 20 + 6
[B]c = 26
[/B]
Therefore, Mike Jacobs hit 20 home runs and Miguel Cabrera hit 26 home runs.

Dwayne earn $6 for each hour of yard work. After doing a total of 3 hours of yard work, how much mon

Dwayne earn $6 for each hour of yard work. After doing a total of 3 hours of yard work, how much money will Dwayne have earned?
We're given the hourly earnings equation below:
Hourly Earnings = Hourly Rate * hours worked
Hourly Earnings = $6 * 3
Hourly Earnings = [B]$18[/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]

Earnings Before Interest and Taxes (EBIT) and Net Income

Given inputs of sales, fixed costs, variable costs, depreciation, and taxes, this will determine EBIT and Net Income and Profit Margin

Ellipses

Given an ellipse equation, this calculates the x and y intercept, the foci points, and the length of the major and minor axes as well as the eccentricity.

Equation of a Plane

Given three 3-dimensional points, this calculates the equation of a plane that contains those points.

Equilateral Triangle

Given a side (a), this calculates the following items of the equilateral triangle:

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h_{a},h_{b},h_{c})

* medians (m_{a},m_{b},m_{c})

* angle bisectors (t_{a},t_{b},t_{c})

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h

* medians (m

* angle bisectors (t

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

Equivalent Annual Cost (EAC)

Given 2 Items/machines with an Investment Cost, expected lifetime, and maintenance cost, this will calculate the EAC for each Item/machine as well as draw a conclusion on which project to invest in.

Equivalent Fractions

Given a fraction, this will determine equivalent fractions

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]

Estimating Reasonableness of Products

Given a product of 2 numbers and an estimated product, this will check to see if it is reasonable

Euclids Algorithm and Euclids Extended Algorithm

Given 2 numbers a and b, this calculates the following

1) The Greatest Common Divisor (GCD) using Euclids Algorithm

2) x and y in Bézouts Identity ax + by = d using Euclids Extended Algorithm Extended Euclidean Algorithm

1) The Greatest Common Divisor (GCD) using Euclids Algorithm

2) x and y in Bézouts Identity ax + by = d using Euclids Extended Algorithm Extended Euclidean Algorithm

Eulers Totient (φ)

Given a positive integer (n), this calculates Euler's totient, also known as φ

Event Likelihood

Given a probability, this determines how likely that event is

Expand Master and Build Polynomial Equations

This calculator is the __ultimate__ expansion tool to multiply polynomials. It expands algebraic expressions listed below using all 26 variables (a-z) as well as negative powers to handle polynomial multiplication. Includes multiple variable expressions as well as outside multipliers.

Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)^{x}

* Polynomial Expansions c(d + e + f)^{x}

* FOIL Expansions (a + b)(c + d)

* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)

* Polynomial Expansions c(d + e + f)

* FOIL Expansions (a + b)(c + d)

* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)

Expected Frequency

Given a contingency table (two-way table), this will calculate expected frequencies and then determine a conclusion based on a Χ^{2} test with critical value test and conclusion.

F varies directly as g and inversely as r^2

F varies directly as g and inversely as r^2
[U]Givens and assumptions[/U]
[LIST]
[*]We take a constant of variation called k.
[*][I]Varies directly means we multiply our variable term by k[/I]
[*][I]Varies inversely means we divide k by our variable term[/I]
[/LIST]
The phrase varies directly or varies inversely means we have a constant k such that:
[B]F = kg/r^2[/B]

Factorization

Given a positive integer, this calculates the following for that number:

1) Factor pairs and prime factorization and prime power decomposition

2) Factors and Proper Factors 3) Aliquot Sum

1) Factor pairs and prime factorization and prime power decomposition

2) Factors and Proper Factors 3) Aliquot Sum

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]

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 a linear function f, given f(16)=-2 and f(-12)=-9. Then find f(0)

Find a linear function f, given f(16)=-2 and f(-12)=-9. Then find f(0).
We've got 2 points:
(16, -2) and (-12, -9)
Calculate the slope (m) of this line using:
m = (y2 - y1)/(x2 - x1)
m = (-9 - -2)/(-12 - 16)
m = -7/-28
m = 1/4
The line equation is denoted as:
y = mx + b
Let's use the first point (x, y) = (16, -2)
-2 = 1/4(16) + b
-2 = 4 + b
Subtract 4 from each side, and we get:
b = -6
So our equation of the line is:
y = 1/4x - 6
The questions asks for f(0):
y = 1/4(0) - 6
y = 0 - 6
[B]y = -6[/B]

Find an equation of the line containing the given pair of points (1,5) and (3,6)

Find an equation of the line containing the given pair of points (1,5) and (3,6).
Using our[URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=5&slope=+2%2F5&xtwo=3&ytwo=6&pl=You+entered+2+points'] point slope calculator[/URL], we get:
[B]y = 1/2x + 9/2[/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 two numbers word problems

Given two numbers with a sum of s where one number is n greater than another, this calculator determines both numbers.

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]

Fisher Transformation and Fisher Inverse

Given a correlation coefficient (r), this calculates the Fisher Transformation (z).

Given a Fisher Transformation (r), this calculates the Fisher Inverse (r)

Given a Fisher Transformation (r), this calculates the Fisher Inverse (r)

Fishers Exact Test

Given a, b, c, and d, this calculates the probability of any such set of values using Fishers exact Test

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]

Forward Rate

Given two times and two zero-coupon yield rates at those times, this calculates the forward rate.

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]

Fractions and Mixed Numbers

Given (improper fractions, proper fraction, mixed numbers, or whole numbers), this performs the following operations:

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

Free Fall Speed

Given a height, this calculates free fall speed based on gravitational force

Frequency and Wavelength and Photon Energy

Provides the following 3 items using the speed of light and Plancks constant (h):

- Given a frequency of centimeters, feet, meters, or miles the calculator will determine wavelength in Hz, KHz, MHz, GHz

- Given a wavelength of Hz, KHz, MHz, GHz, the calculator will determine frequency in centimeters, feet, meters, or miles

- Calculates photon energy

- Given a frequency of centimeters, feet, meters, or miles the calculator will determine wavelength in Hz, KHz, MHz, GHz

- Given a wavelength of Hz, KHz, MHz, GHz, the calculator will determine frequency in centimeters, feet, meters, or miles

- Calculates photon energy

Functions-Derivatives-Integrals

Given a polynomial expression, this calculator evaluates the following items:

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1^{st} Derivative ƒ'(x) The derivative of your expression will also be evaluated at a point, i.e., ƒ'(1)

3) 2^{nd} Derivative ƒ''(x) The second derivative of your expression will be also evaluated at a point, i.e., ƒ''(1)

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1

3) 2

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

Fundamental Rule of Counting

Given a set of items, this calculates the total number of groups/choices that can be formed using the rule of product.

Gary has three less pets than Abe. If together they own 15 pets, how many pets does Gary own?

Let g = Gary's pets and a = Abe's pets.
We are given two equations:
(1) g = a - 3
(2) a + g = 15
Substitute (1) into (2)
a + (a - 3) = 15
Combine Like Terms:
2a - 3 = 15
Add 3 to each side:
2a = 18
Divide each side by 2 to isolate a:
a = 9 --> Abe has 9 pets
Substitute a = 9 into Equation (1)
g = 9 - 3
g = 6 --> Gary has 6 pets

Gas Mileage

Given miles driven and gallons of gas, this calculates your gas (fuel) mileage.

Gayle has 36 coins, all nickels and dimes, worth $2.40. How many dimes does she have?

Gayle has 36 coins, all nickels and dimes, worth $2.40. How many dimes does she have?
Set up our given equations using n as the number of nickels and d as the number of dimes:
[LIST=1]
[*]n + d = 36
[*]0.05n + 0.1d = 2.40
[/LIST]
Use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+d+%3D+36&term2=0.05n+%2B+0.1d+%3D+2.40&pl=Cramers+Method']simultaneous equations calculator[/URL] to get:
n = 24
[B]d = 12[/B]

Geometric Annuity Immediate

Given an immediate annuity with a geometric progression, this solves for the following items

1) Present Value

2) Accumulated Value (Future Value)

3) Payment

1) Present Value

2) Accumulated Value (Future Value)

3) Payment

Geometric Mean of a Triangle

Given certain segments of a special right triangle, this will calculate other segments using the geometric mean

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]

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(a)=a˛ - 2a - 1 and f(x)=x˛ - 2x, Find: a) f(a+2)-f(a)/2 b) g(a+h)-g(a)/h

Given g(a)=a˛ - 2a - 1 and f(x)=x˛ - 2x:
Find:
a) f(a+2) - f(a)/2
b) g(a+h) - g(a)/h
a) f(a + 2) = (a + 2)^2 - 2(a + 2)
f(a + 2) = a^2 + 2a + 4 - 2a - 4
Simplify and combine like terms:
the 2a and 4's cancel, so we have:
f(a + 2) = a^2
f(a)/2 = (a^2 - 2a)/2
Subtract one from the other, we get:
a^2 - a^2/2 - a
[B]a) a^2/2 - a
------------------------[/B]
b) g(a + h) = (a + h)^2 - 2(a + h) - 1
g(a + h) = a^2 +2ah + h^2 - 2a - 2h - 1
g(a)/2 = (a^2 - 2a - 1)/h
g(a)/2 = (a^2 - 2a - 1)/h
Subtract one from the other:
g(a+h) - g(a)/h
a^2 +2ah + h^2 - 2a - 2h - 1 - (a^2 - 2a - 1)/h
Multiply through by h
[B]a^2h + 2ah^2 + h^3 - 2ah - 2h^2 - h - a^2 + 2a + 1[/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 P(A) = 0.37, find P ( not A )

Given P(A) = 0.37, find P ( not A )
Not A is also written as A'.
We use the formula below:
P(A') = 1 - P(A)
P(A') = 1 - 0.37
P(A') = [B]0.63[/B]

Given that E[Y]=2 and Var [Y] =3, find E[(2Y + 1)^2]

Given that E[Y]=2 and Var [Y] =3, find E[(2Y + 1)^2]
Multiply through
E[(2Y + 1)^2] = E[4y^2 + 4y + 1]
We can take the expected value of each term
E[4y^2] + E[4y] + E[1]
For the first term, we have:
4E[Y^2]
We define the Var[Y] = E[Y^2] - (E[Y])^2
Rearrange this term, we have E[Y^2] = Var[Y] + (E[Y])^2
E[Y^2] = 3+ 2^2
E[Y^2] = 3+ 4
E[Y^2] = 7
So our first term is 4(7) = 28
For the second term using expected value rules of separating out a constant, we have
4E[Y] = 4(2) = 8
For the third term, we have:
E[1] = 1
Adding up our three terms, we have:
E[4y^2] + E[4y] + E[1] = 28 + 8 + 1
E[4y^2] + E[4y] + E[1] = [B]37[/B]

Given that P (A)=0.6, P (B)=0.5, P (A|B) = 0.2, P (C|A)= 0.3 and P (C|B)=0.4. (1) If they are depe

Given that P (A)=0.6, P (B)=0.5, P (A|B) = 0.2, P (C|A)= 0.3 and P (C|B)=0.4.
(1) If they are dependent each other, what is P (B | A) = ?
(2) If the event C is conditionally dependent upon evens A and B, What's the probability: P (A|C) = ?
(1) Bayes Rule: P(B|A) = P(B) * P(A|B)
P(B|A) = 0.5 * 0.2 = 0.1
(2) Bayes Rule: P(A|C) = P(A) * P(C|A)
P(A|C)= 0.6 * 0.3 = 0.18

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]

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.
[IMG]http://www.mathcelebrity.com/images/math_problem_library_129.png[/IMG]
If AB = 6 and AD = 8, by the Pythagorean theorem, we have BD = 10 from our [URL='http://www.mathcelebrity.com/pythag.php?side1input=6&side2input=8&hypinput=&pl=Solve+Missing+Side']Pythagorean Theorem[/URL] Calculator
Using that, we have another right triangle which we can use the [URL='http://www.mathcelebrity.com/pythag.php?side1input=10&side2input=24&hypinput=&pl=Solve+Missing+Side']pythagorean theorem[/URL] calculator to get [B]FD = 26[/B]

Given w(x) = 3x + 8, find w(2b + 6).

Given w(x) = 3x + 8, find w(2b + 6).
Plug the value of 2b + 6 in for x
w(2b + 6) = 3(2b + 6) + 8
Multiply through:
w(2b + 6) = 6b + 18 + 8
Group like terms:
w(2b + 6) = [B]6b + 26[/B]

Given y= 4/3x what is the constant of proportionality

Given y= 4/3x what is the constant of proportionality
Direct variation means the constant of proportionality is y/x.
Cross multiplying, we get:
y/x = [B]4/3[/B]

Given: 3(2x ? 5) = 15 Prove: x = 5

Given: 3(2x ? 5) = 15 Prove: x = 5
Set x = 5:
3(2(5) - 5)
3(10 - 5)
3(5)
15
So if x = 5, then:
3(2x ? 5) = 15

Given: 9 - 4x = -19 Prove: x = 7

Given: 9 - 4x = -19 Prove: x = 7
Solve for [I]x[/I] in the equation 9 - 4x = - 19
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 9 and -19. To do that, we subtract 9 from both sides
-4x + 9 - 9 = -19 - 9
[SIZE=5][B]Step 2: Cancel 9 on the left side:[/B][/SIZE]
-4x = -28
[SIZE=5][B]Step 3: Divide each side of the equation by -4[/B][/SIZE]
-4x/-4 = -28/-4
x = [B]7[/B]

Given:

Given:

Given: BC = EF
AC = EG
AB = 10
BC = 3
Prove FG = 10
[LIST]
[*]AC = AB + BC (Segment Addition Postulate)
[*]AB = 10, BC = 3 (Given)
[*]AC = 10 + 3 (Substitution Property of Equality)
[*]AC = 13 (Simplify)
[*]AC = EG, BC = EF (Given)
[*]EG = 13, EF = 3 (Segment Equivalence)
[*]EG = EF + FG (Segment Addition Postulate)
[*]13 = 3 + FG (Substitution Property of Equality)
[*]FG = 10 (Subtraction Property)
[/LIST]

Given: WS bisects

Given: WS bisects

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]

Greatest Common Factor and Least Common Multiple

Given 2 or 3 numbers, the calculator determines the following:

* Greatest Common Factor (GCF) using Factor Pairs

* Rewrite Sum using the Distributive Property and factoring out the GCF

* Least Common Multiple (LCM) / Least Common Denominator (LCD) using Factor Pairs

* GCF using the method of Successive Division

* GCF using the Prime Factorization method

* Determine if the numbers are coprime and twin prime

* Greatest Common Factor (GCF) using Factor Pairs

* Rewrite Sum using the Distributive Property and factoring out the GCF

* Least Common Multiple (LCM) / Least Common Denominator (LCD) using Factor Pairs

* GCF using the method of Successive Division

* GCF using the Prime Factorization method

* Determine if the numbers are coprime and twin prime

Group Combinations

Given an original group of certain types of member, this determines how many groups/teams can be formed using a certain condition.

Gym Class Team Generator

Given a list of players, this will randomly generate two teams.

Half of a pepperoni pizza plus 3/4ths of a ham and pineapple pizza has 765 calories. 1/4th of a pepp

Half of a pepperoni pizza plus 3/4ths of a ham and pineapple pizza has 765 calories. 1/4th of a pepperoni pizza and a whole ham and pineapple pizza contains 745 calories. How many calories are each of the 2 kinds of pizzas individually?
Let p be the pepperoni pizza calories and h be the ham and pineapple pizza calories. We're given
[LIST=1]
[*]0.5p + 0.75h = 765
[*]0.25p + h = 745
[/LIST]
With this system of equations, we can solve using 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.5p+%2B+0.75h+%3D+765&term2=0.25p+%2B+h+%3D+745&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.5p+%2B+0.75h+%3D+765&term2=0.25p+%2B+h+%3D+745&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.5p+%2B+0.75h+%3D+765&term2=0.25p+%2B+h+%3D+745&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[B]h = 580
p = 660[/B]

Half-Life of a Substance

Given a half-life (h) of a substance at time t, this determines the new substance size at time t_{n}, otherwise known as decay.

Hardy-Weinberg

Given a dominant gene frequency probability of p, this displays the Punnet Square Hardy Weinberg frequencies

Heat Index

Given a temperature in Fahrenheit and a relative humidity percentage, this calculates the Heat Index.

HELP SOLVE

A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level.
x = 20.5, n = 11, ? = 7, H0: µ = 18.7 , Ha: µ ? 18.7 , ? = 0.01

HELP SOLVE

sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level.
x = 3.7, n = 32, ? = 1.8, H0: µ = 4.2 , Ha: µ ? 4.2 , ? = 0.05

HELP SOLVE

A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test about the mean, µ, of the population from which the sample was drawn
x = 3.26 , S = 0.55, ?N= 9, H0: µ = 2.85, Ha: µ > 2.85 , ? = 0.01

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]

Herfindahl Index

Given a market share of a set of companies, this determines the Herfindahl Index and Normalized Herfindahl Index.

Hexagon

This calculator solves for side length (s), Area (A), and Perimeter (P) of a hexagon given one of the 3 entries.

Hope it's okay to ask this here?

A candy vendor analyzes his sales records and ?nds that if he sells x candy bars in one day, his pro?t(in dollars) is given byP(x) = ? 0.001x2 + 3x ? 1800
(a.) Explain the signi?cance of the number 1800 to the vendor.
(b.) What is the maximum pro?t he can make in one day, and how many candy bars must he sell to
achieve it?
I got 1800 as the amount he starts with, and can't go over. maximum pro?t as 4950
and if I got that right I am getting stuck on how to find how many candy bars.
Thanks

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]

Hyperbola

Given a hyperbola equation, this calculates:

* Equation of the asymptotes

* Intercepts

* Foci (focus) points

* Eccentricity ε

* Latus Rectum

* semi-latus rectum

* Equation of the asymptotes

* Intercepts

* Foci (focus) points

* Eccentricity ε

* Latus Rectum

* semi-latus rectum

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 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 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]

If $349,000 is given to 10 people how much does each person get?

If $349,000 is given to 10 people how much does each person get?
Each person gets $349,000 / 10 = [B]$34,900[/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 & 1/2 pounds of walnuts cost $2.50, how much do walnuts cost per pound?

If 2 & 1/2 pounds of walnuts cost $2.50, how much do walnuts cost per pound?
Calculate unit cost given that 2 & 1/2 = 2.5:
2.50 per pound / 2.5 pounds = [B]$1 per pound[/B]

If 3x - y = 12, what is the value of 8^x/2^y

If 3x - y = 12, what is the value of 8^x/2^y
We know 8 = 2^3
So using a rule of exponents, we have:
(2^3)^x/2^y
2^(3x)/2^y
Using another rule of exponents, we rewrite this fraction as:
2^(3x -y)
We're given 3x - y = 12, so we have:
[B]2^12[/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 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 universal set contains 250 elements, n(A) = 90, n(B) = 125, and n(A ? B) = 35, find n(A ? B)'.

If a universal set contains 250 elements, n(A) = 90, n(B) = 125, and n(A ? B) = 35, find n(A ? B)'.
We know from set theory that:
n(A U B) = n(A) + n(B) - n(A ? B)
Plugging in our given values, we get:
n(A U B) = 90 + 125 - 35
n(A U B) = 180
The problem asks for n(A U B)'. This formula is found with:
n(A U B)' = n(U) - n(A U B)
n(U) is the universal set which is 250, so we have:
n(A U B)' = 250 - 180
n(A U B)' = [B]70[/B]

If FG = 9, GH = 4x, and FH = 7x, what is GH?

If FG = 9, GH = 4x, and FH = 7x, what is GH?
By segment addition, we have:
FG + GH = FH
Substituting in the values given, we have:
9 + 4x = 7x
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%2B4x%3D7x&pl=Solve']type it in our math engine[/URL] and we get:
x = 3
The question asks for GH, so with x = 3, we have:
GH = 4(3)
GH = [B]12[/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 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 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 JK = PQ and PQ = ST, then JK=ST

If JK = PQ and PQ = ST, then JK=ST
JK = PQ | Given
Substitute ST for PQ since PQ = ST | Substitution
[B]JK = ST[/B]

If Mr hernandez has 5 times as many students as Mr daniels and together they have 150 students how m

If Mr hernandez has 5 times as many students as Mr daniels and together they have 150 students how many students do each have?
Let h = Mr. Hernandez's students and d = Mr. Daniels students.
We are given two equations:
(1) h = 5d
(2) d + h = 150
Substitute equation (1) into equation (2)
d + (5d) = 150
Combine like terms:
6d = 150
Divide each side of the equation by 6 to isolate d
d = 25 <-- Mr. Daniels Students
Now, plug the value for d into equation (1)
h = 5(25)
h = 125 <-- Mr. Hernandez students

if n(A) = 6, n(A intersect B) = 2 and n(A union B) = 11, find n(B)

if n(A) = 6, n(A intersect B) = 2 and n(A union B) = 11, find n(B).
n(A union B) = n(A) + n(B) - n(A intersect B)
Plugging in our given values, we have:
11 = 6 + n(B) - 2
11 = 4 + n(B)
Subtract 4 from each side:
[B]n(B) = 7[/B]

If n(A)=1200, n(B)=1250 and n(AintersectionB)=320, then n(AUB) is

If n(A)=1200, n(B)=1250 and n(AintersectionB)=320, then n(AUB) is
We know that:
n(AUB) = n(A) + n(B) - n(AintersectionB)
Plugging in our given numbers, we get:
n(AUB) = 1200 + 1250 - 320
n(AUB) = [B]2130[/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 sc = hr and hr=ab then sc=ab

if sc = hr and hr=ab then sc=ab
sc = hr (given)
Since hr = ab, we can substitute ab for hr by substitution:
[B]sc = ab[/B]

If the circumference of a circular rug is 16? feet, then what is the area of the rug in terms of pi

If the circumference of a circular rug is 16? feet, then what is the area of the rug in terms of pi
C = 2pir, so we have:
C = 16?
16? = 2?r
Divide each side by 2?:
r = 16?/2?
r = 8
Now, the area of a circle A is denoted below:
A = ?r^2
Given r = 8 from above, we have:
A = ?(8)^2
A = [B]64?[/B]

If the diameter of a circle is n, what is the circumference?

If the diameter of a circle is n, what is the circumference?
Diameter of a circle = pi(d)
Given d = n, we have:
Diameter = pi(n)

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 probability of an event occurring is 7%, what is the probability of an event not occurring?

If the probability of an event occurring is 7%, what is the probability of an event not occurring?
The probability of all event is 1, or 100%.
If we treat the success of an event as p, then q is 1 - p.
Using percentages, we have:
q = 100% - p
Given p = 7%, we have:
q = 100% - 7%
q = [B]93%[/B]

if the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?

if the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?
Set up our given ratio:
2x/5y = 3/4
Cross multiply:
2x * 4 = 5y * 3
8x = 15y
Divide each side by 8:
8x/8 = 15y/8
x = 15y/8
Now divide each side by y to find x/y:
x/y = 15y/8y
x/y =[B] 15/8[/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 = 2y/3 and y = 18, what is the value of 2x - 3?

If x = 2y/3 and y = 18, what is the value of 2x - 3?
A) 21
B) 15
C) 12
D) 10
Substitute the values into the equation:
2(2y/3) - 3 <-- Given x = 2y/3
Simplifying, we have:
4y/3 - 3
Now substitute y = 18 into this:
4(18)/3 - 3
4(6) - 3
24 - 3
[B]21 or Answer A[/B]

If you divide my brother's age by 3 and then add 20, you will get my age, which is 31. What is my br

If you divide my brother's age by 3 and then add 20, you will get my age, which is 31. What is my brothers age?
Let b be the brother's age.
We're given the following relationship for the brother's age and my age:
b/3 + 20 = 31
Subtract 20 from each side:
b/3 + 20 - 20 = 31 - 20
Cancel the 20's on the left side and we get:
b/3 = 11
Cross multiply, and we get:
b = 3 * 11
b = [B]33
[/B]
Check our work using b = 33 for b/3 + 20 = 31:
33/3 + 20 ? 31
11 + 20 ? 31
31 = 31

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]

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 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 class there are 5 more boys than girls. There are 13 students in all. How many boys are there i

In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there in the class?
We start by declaring variables for boys and girls:
[LIST]
[*]Let b be the number of boys
[*]Let g be the number of girls
[/LIST]
We're given two equations:
[LIST=1]
[*]b = g + 5
[*]b + g = 13
[/LIST]
Substitute equation (1) for b into equation (2):
g + 5 + g = 13
Grouping like terms, we get:
2g + 5 = 13
Subtract 5 from each side:
2g + 5 - 5 = 13 - 5
Cancel the 5's on the left side and we get:
2g = 8
Divide each side of the equation by 2 to isolate g:
2g/2 = 8/2
Cancel the 2's on the left side and we get:
g = 4
Substitute g = 4 into equation (1) to solve for b:
b = 4 + 5
b = [B]9[/B]

In a factory that manufactures tires, a machine responsible for molding the tire has a failure rate

In a factory that manufactures tires, a machine responsible for molding the tire has a failure rate of 0.2%. If 1,000 tires are produced in a day, of which 6 are faulty, what is the difference between the experimental probability and the theoretical probability?
Theoretical probability = Failure Rate * Tires
Theoretical probability = 0.002 * 1000
Theoretical probability = 2
The experimental probability was given as 6, so the difference is:
6 - 2 = [B]4[/B]

In a given year, Houston has good air quality 48% of the days, moderate air quality 41% of the days,

In a given year, Houston has good air quality 48% of the days, moderate air quality 41% of the days, and unhealthy air quality 4% of the days. How many days per year do residents have unhealthy air quality?
4% of 365 days in a year = [B]14.6 days. If we are talking full days, we have 14.[/B]

In a golf tournament Ned was 4 under par on Saturday and 5 over or on Sunday. What is the difference

In a golf tournament Ned was 4 under par on Saturday and 5 over or on Sunday. What is the difference in his score on Sunday compared to his score on Saturday
Givens and opening thoughts:
[LIST]
[*]Think of par as 0 or average.
[*]Under par is negative
[*]Over par is positive
[*]We have 4 under par as -4
[*]We have 5 over par as +5
[/LIST]
The difference is found by subtracting:
+5 - -4
+5 + 4
[B]9 strokes[/B]

In a hurricane the wind pressure varies directly as the square of the wind velocity. If a wind pres

In a hurricane the wind pressure varies directly as the square of the wind velocity. If a wind pressure is a measure of a hurricane's destruction capacity, what happens to this destructive power when the wind speed doubles?
Let P = pressure and v = velocity (wind speed)
We are given p = v^2
Double velocity, so we have a new pressure P2:
P2 = (2v)^2
P2 = 4v^2
Compare the 2:
p = v^2
p = 4v^2
Doubling the wind speed [B]quadruples, or 4 times[/B] the pressure.

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 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 x years time, Peter will be 23 years old. How old is he now?

In x years time, Peter will be 23 years old. How old is he now?
Let Peter's current age be a. In x years time means we add x to a, so we're given:
a + x = 23
We want to find a, s we subtract x from each side to get:
a + x - x = 23 - x
Cancel the x terms on the left side and we get:
a = [B]23 - x[/B]

Inclusive Number Word Problems

Given an integer A and an integer B, this calculates the following inclusive word problem questions:

1) The Average of all numbers inclusive from A to B

2) The Count of all numbers inclusive from A to B

3) The Sum of all numbers inclusive from A to B

1) The Average of all numbers inclusive from A to B

2) The Count of all numbers inclusive from A to B

3) The Sum of all numbers inclusive from A to B

Incremental Cash Flow

Given cash inflows, outflows, depreciable amounts, and tax rates, this determines the incremental cash flows.

Input Table

Given an input table with input and output values, this will determine the operator and rule used to populate the missing values.

Installment Sales Method of Accounting

Given a sales price, cost amount, installment payment amount and term, this will show the accounting for the Installment Payment method.

Interpolation

Given a set of data, this interpolates using the following methods:

* Linear Interpolation

* Nearest Neighbor (Piecewise Constant)

* Polynomial Interpolation

* Linear Interpolation

* Nearest Neighbor (Piecewise Constant)

* Polynomial Interpolation

Interval Partition

Given a partitioned interval, this evaluates the norm (mesh) by calculating each subinterval

Isosceles Triangle

Given a long side (a) and a short side (b), this determines the following items of the isosceles triangle:

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

It costs $4.25 per game at the bowling alley plus $1.90 to rent shoes. if Wayne has $20, how many ga

It costs $4.25 per game at the bowling alley plus $1.90 to rent shoes. if Wayne has $20, how many games can he Bowl?
Let g be the number of games. The cost for Wayne is:
C(g) = Cost per game * number of games + shoe rental
4.25g + 1.90 = C(g)
We're given C(g) = 20, so we have:
4.25g + 1.90 = 20
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=4.25g%2B1.90%3D20&pl=Solve']equation solver[/URL] for g, we get:
g = 4.25
We need whole games, we we round down to [B]4 games[/B]

Jack has 34 bills and coins in 5’s and 2’s. The total value is $116. How many 5 dollar bills does he

Jack has 34 bills and coins in 5’s and 2’s. The total value is $116. How many 5 dollar bills does he have?
Let the number of 5 dollar bills be f. Let the number of 2 dollar bills be t. We're given two equations:
[LIST=1]
[*]f + t = 34
[*]5f + 2t = 116
[/LIST]
We have a system of equations, which we can solve 3 ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answers:
[LIST]
[*][B]f = 16[/B]
[*][B]t = 18[/B]
[/LIST]

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]

Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episod

Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episode airs, Jake receives a bunch of fan mail. He splits all the letters into 3 equal stacks to open with his mom and his sister. Each stack contains 21 letters. Which equation can you use to find the number of letters n Jake receives?
The number of letters n is represented by number of stacks (s) times letter per stack (l). We're given s = 3 and l = 21, so we have:
n = 21(3)
n = [B]63[/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]

Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling?

Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling?
Distance = Rate * Time
We're given D = 395 and t = 5
We want Rate. We divide each side of the equation by time:
Distance / Time = Rate * Time / Time
Cancel the Time's on each side and we get:
Rate = Distance / Time
Plugging our numbers in, we get:
Rate = 395/5
Rate = [B]79 kilometers[/B]

Jason has an equal number of nickels and dimes. The total value of his nickels and dimes is $2.25. H

Jason has an equal number of nickels and dimes. The total value of his nickels and dimes is $2.25. How many nickels does Jason have?
Let the number of nickels be n
Let the number of dimes be d
We're given two equations:
[LIST=1]
[*]d = n
[*]0.05n + 0.1d = 2.25
[/LIST]
Substitute equation (1) for d into equation (2):
0.05n + 0.1n = 2.25
Solve for [I]n[/I] in the equation 0.05n + 0.1n = 2.25
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(0.05 + 0.1)n = 0.15n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
0.15n = + 2.25
[SIZE=5][B]Step 3: Divide each side of the equation by 0.15[/B][/SIZE]
0.15n/0.15 = 2.25/0.15
n = [B]15[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05n%2B0.1n%3D2.25&pl=Solve']Source[/URL]

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 has 26 less than triple the savings of Matthew. Matthew has saved 81. How much has Jennifer

Jennifer has 26 less than triple the savings of Matthew. Matthew has saved 81. How much has Jennifer saved?
Let Jennifer's savings be j. We're given:
j = 3(81) - 26
j = 243 - 26
j = [B]217[/B]

Jennifer is twice as old as Peter. The difference between their ages is 15. What is Peters age

Jennifer is twice as old as Peter. The difference between their ages is 15. What is Peters age
Let j be Jennifer's age
Let p be Peter's age
We're given two equations:
[LIST=1]
[*]j = 2p
[*]j - p = 15
[/LIST]
Substitute equation (1) into equation (2) for j
2p - p = 15
To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=2p-p%3D15&pl=Solve']type this equation into our calculation engine[/URL] and we get:
p = [B]15[/B]

Jenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combined

Jenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combined distance thrown by the 3 friends is 124 metres, how far did Angus throw the javelin?
Assumptions and givens:
[LIST]
[*]Let a be the distance Angus threw the javelin
[*]Let c be the distance Cameron threw the javelin
[*]Let j be the distance Jenny threw the javelin
[/LIST]
We're given 3 equations:
[LIST=1]
[*]j = a + 4
[*]j = c - 5
[*]a + c + j = 124
[/LIST]
Since j is the common variable in all 3 equations, let's rearrange equation (1) and equation (2) in terms of j as the dependent variable:
[LIST=1]
[*]a = j - 4
[*]c = j + 5
[*]a + c + j = 124
[/LIST]
Now substitute equation (1) and equation (2) into equation (3) for a and c:
j - 4 + j + 5 + j = 124
To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=j-4%2Bj%2B5%2Bj%3D124&pl=Solve']type it in our math engine[/URL] and we get:
j = 41
The question asks how far Angus (a) threw the javelin. Since we have Jenny's distance j = 41 and equation (1) has j and a together, let's substitute j = 41 into equation (1):
a = 41 - 4
a = [B]37 meters[/B]

Jill and Jack are getting vegetables from the Farmer's Market. Jill buys 12 carrots and 8 tomatoes f

Jill and Jack are getting vegetables from the Farmer's Market. Jill buys 12 carrots and 8 tomatoes for $34. Jack buys 10 carrots and 7 tomatoes for $29. How much does each carrot and each tomato cost?
Let the cost of carrots be c and the cost of tomatoes be t. Since the total cost is price times quantity, We're given two equations:
[LIST=1]
[*]12c + 8t = 34 <-- Jill
[*]10c + 7t = 29 <-- Jack
[/LIST]
We have a system of equations. We can solve this one of three ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]t = 2[/B]
[*][B]c = 1.5[/B]
[/LIST]

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]

Jim works for his dad and earns $400 every week plus $22 for every chair (c) he sells. Write an equa

Jim works for his dad and earns $400 every week plus $22 for every chair (c) he sells. Write an equation that can be used to determine jims weekly salary (S) given the number of chairs (c) he sells.
[B]S(c) = 400 + 22c[/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]

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 76 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this.
At least means greater than or equal to, so we have:
[B]3x + 4y >= 76[/B]

Joe worked in a shoe department where he earned $325 weekly and 6.5% commission on all of his sales.

Joe worked in a shoe department where he earned $325 weekly and 6.5% commission on all of his sales. What was joe’s total sales if he earned $507 last week
Let s be total Sales. 6.5% is 0.065 as a decimal, so Joe's earnings are given by:
0.065s + 325 = 507
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.065s%2B325%3D507&pl=Solve']type this equation into our math engine[/URL] and we get:
s = [B]2800[/B]

Joel bought 88 books. Some books cost $13 each and some cost $17 each. In all, he spent $128. Which

Joel bought 88 books. Some books cost $13 each and some cost $17 each. In all, he spent $128. Which system of linear equations represents the given situation?
Let a be the number of the $13 book, and b equal the number of $17 books. We have the following system of linear equations:
[LIST=1]
[*][B]a + b = 88[/B]
[*][B]13a + 17b = 128[/B]
[/LIST]
To solve this system, use our calculator for the following methods:
[LIST]
[*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Substitution']Substitution[/URL]
[*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Elimination']Elimination[/URL]
[*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]

Joey and Romnick play in the same soccer team. Last Saturday, Romnick scored 3 more goals than Joey,

Joey and Romnick play in the same soccer team. Last Saturday, Romnick scored 3 more goals than Joey,but together they scored less than 9 goals. What are the possible number of goal Romnick scored?
Let j be Joey's goals
Let r by Romnick's goals
We're given 1 equation and 1 inequality:
[LIST=1]
[*]r = j + 3
[*]r + j < 9
[/LIST]
Rearranging equation 1 for j, we have:
[LIST=1]
[*]j = r - 3
[*]r + j < 9
[/LIST]
Substitute equation (1) into inequality (2) for j:
r + r - 3 < 9
2r - 3 < 9
[URL='https://www.mathcelebrity.com/1unk.php?num=2r-3%3C9&pl=Solve']Typing this inequality into our math engine[/URL], we get:
[B]r < 6[/B]

Joint Variation Equations

Given a joint variation (jointly proportional) of a variable between two other variables with a predefined set of conditions, this will create the joint variation equation and solve based on conditions.
Also called combined variation.

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]

Juan is going on a flight to the beach. his luggage weighs 36 pounds. The bag weighs 4 pounds more t

Juan is going on a flight to the beach. his luggage weighs 36 pounds. The bag weighs 4 pounds more than the weight of 2 small bags of beach toys. Which equation can be used to find the weight in pounds of each bag of beach toys?
Let b be the weight of each bag of beach toys. We're given the following relationship:
2b -4 = 36
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=2b-4%3D36&pl=Solve']type it in our math engine[/URL] and we get:
b = [B]20[/B]

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and .10 cents for additional texts. How many texts did she send out?
Let m be the number of messages. We have a cost function of:
C(m) = 9 + 0.1(m - 600)
We are given C(m) = 18.20
18.20 = 9 + 0.1(m - 600)
18.20 = 9 + 0.1m - 60
Combine like terms:
18.20 = 0.1m - 51
Add 51 to each side
0.1m = 69.20
Divide each side by 0.1
[B]m = 692[/B]

Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. Wh

Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. What age is Martina?
[U]Assumptions and givens:[/U]
[LIST]
[*]Let Justin's age be j
[*]Let Martina's age be m
[*]j > m ([I]since Justin is older than Martina[/I])
[/LIST]
We're given the following equations :
[LIST=1]
[*]j - m = 22
[*]j + m = 54
[/LIST]
Since the coefficients of m are opposites, we can take a shortcut using the [I]elimination method[/I] and add equation (1) to equation (2)
(j + j) + (m - m) = 22 + 54
2j = 76
To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%3D76&pl=Solve']type this equation into our math engine[/URL] and we get:
j = 38
The question asks for Martina's age (m), so we can pick equation (1) or equation (2). Let's use equation (1):
38 - m = 22
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=38-m%3D22&pl=Solve']type it in our math engine[/URL] and we get:
m = [B]16[/B]

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft squared. What are the dimensions of the kennel? How many feet of fencing did she use? Explain.
Area of a square with side length (s) is:
A = s^2
Given A = 64, we have:
s^2 = 64
[URL='https://www.mathcelebrity.com/radex.php?num=sqrt(64%2F1)&pl=Simplify+Radical+Expression']Typing this equation into our math engine[/URL], we get:
s = 8
Which means the dimensions of the kennel are [B]8 x 8[/B].
How much fencing she used means perimeter. The perimeter P of a square with side length s is:
P = 4s
[URL='https://www.mathcelebrity.com/square.php?num=8&pl=Side&type=side&show_All=1']Given s = 8, we have[/URL]:
P = 4 * 8
P = [B]32[/B]

kate is twice as old as her sister mars. the sum of their ages is 24. find their ages.

kate is twice as old as her sister mars. the sum of their ages is 24. find their ages.
Let k be Kate's age
Let m be Mars's age
We're given two equations:
[LIST=1]
[*]k = 2m. (Because twice means multiply by 2)
[*]k + m = 24
[/LIST]
Substitute equation (1) for k into equation (2):
2m + m = 24
T o solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=2m%2Bm%3D24&pl=Solve']type this equation into our math engine[/URL]:
m = [B]8
[/B]
We want to solve for k using m= 8. Substitute this into equation 1
k = 2(8)
k = [B]16
[/B]
Check our work for equation 1
16 = 2 * 8
16 = 16
Check our work for equation 2
16 + 8 ? 24
24 = 24
[MEDIA=youtube]TJMTRYP-Ct8[/MEDIA]

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]

Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of sla

Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of slacks and paid11.45. Then she brought 5 shirts, 3 pairs of slacks, and 1 sports coat and paid 27.41. Finally, she brought 5 shirts and 1 sports coat and paid 16.94. How much was she charged for each shirt, each pair of slacks, and each sports coat?
Let s be the cost of shirts, p be the cost of slacks, and c be the cost of sports coats. We're given:
[LIST=1]
[*]4s + p = 11.45
[*]5s + 3p + c = 27.41
[*]5s + c = 16.94
[/LIST]
Rearrange (1) by subtracting 4s from each side:
p = 11.45 - 4s
Rearrange (3)by subtracting 5s from each side:
c = 16.94 - 5s
Take those rearranged equations, and plug them into (2):
5s + 3(11.45 - 4s) + (16.94 - 5s) = 27.41
Multiply through:
5s + 34.35 - 12s + 16.94 - 5s = 27.41
[URL='https://www.mathcelebrity.com/1unk.php?num=5s%2B34.35-12s%2B16.94-5s%3D27.41&pl=Solve']Group like terms using our equation calculator [/URL]and we get:
[B]s = 1.99 [/B] <-- Shirt Cost
Plug s = 1.99 into modified equation (1):
p = 11.45 - 4(1.99)
p = 11.45 - 7.96
[B]p = 3.49[/B] <-- Slacks Cost
Plug s = 1.99 into modified equation (3):
c = 16.94 - 5(1.99)
c = 16.94 - 9.95
[B]c = 6.99[/B] <-- Sports Coat cost

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]

Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The tot

Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The total value of the jar is $7.85. How many of each type?
Let d be dimes and q be quarters. Set up two equations from our givens:
[LIST=1]
[*]d + q = 41
[*]0.1d + 0.25q = 7.85
[/LIST]
[U]Rearrange (1) by subtracting q from each side:[/U]
(3) d = 41 - q
[U]Now, substitute (3) into (2)[/U]
0.1(41 - q) + 0.25q = 7.85
4.1 - 0.1q + 0.25q = 7.85
[U]Combine q terms[/U]
0.15q + 4.1 = 7.85
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.15q%2B4.1%3D7.85&pl=Solve']equation calculator[/URL], we get:[/U]
[B]q = 25[/B]
[U]Substitute q = 25 into (3)[/U]
d = 41 - 25
[B]d = 16[/B]

Kevin ran 4 miles more than Steve ran. The sum of their distances is 26 miles. How far did Steve run

Kevin ran 4 miles more than Steve ran. The sum of their distances is 26 miles. How far did Steve run? The domain of the solution is:
Let k be Kevin's miles ran
Let s be Steve's miles ran
We have 2 given equtaions:
[LIST=1]
[*]k = s + 4
[*]k + s = 26
[/LIST]
Substitute (1) into (2)
(s + 4) + s = 26
2s + 4 = 26
Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=2s%2B4%3D26&pl=Solve']equation calculator[/URL] and we get s = 11

Kiko is now 6 times as old as his sister. In 6 years, he will be 3 times as old as his sister. What

Kiko is now 6 times as old as his sister. In 6 years, he will be 3 times as old as his sister. What is their present age?
Let k be Kiko's present age
Let s be Kiko's sisters age.
We're given two equations:
[LIST=1]
[*]k = 6s
[*]k + 6 = 3(s + 6)
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for k:
6s + 6 = 3(s + 6)
[URL='https://www.mathcelebrity.com/1unk.php?num=6s%2B6%3D3%28s%2B6%29&pl=Solve']Typing this equation into our math engine[/URL] to solve for s, we get:
s = [B]4[/B]
To solve for k, we substitute s = 4 into equation (1) above:
k = 6 * 4
k = [B]24[/B]

Kimberly wants to become a member of the desert squad at a big catering company very badly, but she

Kimberly wants to become a member of the desert squad at a big catering company very badly, but she must pass three difficult tests to do so. On the first Terrifying Tiramisu test she scored a 68. On the second the challenging Chocalate-Sprinkled Creme Brulee she scored a 72. If kimberly needs an average of 60 on all three tests to become a member on the squad what is the lowest score she can make on her third and final test
This is a missing average problem.
Given 2 scores of 68, 72, what should be score number 3 in order to attain an average score of 60?
[SIZE=5][B]Setup Average Equation:[/B][/SIZE]
Average = (Sum of our 2 numbers + unknown score of [I]x)/[/I]Total Numbers
60 = (68 + 72 + x)/3
[SIZE=5][B]Cross Multiply[/B][/SIZE]
68 + 72 + x = 60 x 3
x + 140 = 180
[SIZE=5][B]Subtract 140 from both sides of the equation to isolate x:[/B][/SIZE]
x + 140 - 140 = 180 - 140
x = [B]40[/B]

Kinematic Equations

Given the 5 inputs of the 4 kinematic equations, this will solve any of the equations it can based on your inputs for the kinematics.

Kites

This calculates perimeter and/or area of a kite given certain inputs such as short and long side, short and long diagonal, or angle between short and long side

Kris wants to fence in her square garden that is 40 feet on each side. If she places posts every 10

Kris wants to fence in her square garden that is 40 feet on each side. If she places posts every 10 feet, how many posts will she need?
Perimeter (P) of a square with side s:
P = 4s
Given s = 40, we have:
P = 4(40)
P = 160 feet
160 feet / 10 foot spaces = [B]16 posts[/B]

larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2

larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2 numbers
Declare Variables for each number:
[LIST]
[*]Let l be the larger number
[*]Let s be the smaller number
[/LIST]
We're given two equations:
[LIST=1]
[*]l = s + 12
[*]l + s = 74
[/LIST]
Equation (1) already has l solved for. Substitute equation (1) into equation (2) for l:
s + 12 + s = 74
Solve for [I]s[/I] in the equation s + 12 + s = 74
[SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE]
(1 + 1)s = 2s
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
2s + 12 = + 74
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 12 and 74. To do that, we subtract 12 from both sides
2s + 12 - 12 = 74 - 12
[SIZE=5][B]Step 4: Cancel 12 on the left side:[/B][/SIZE]
2s = 62
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2s/2 = 62/2
s = [B]31[/B]
To solve for l, we substitute in s = 31 into equation (1):
l = 31 + 12
l = [B]43[/B]

larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?

larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?
Declare variables for the 2 numbers:
[LIST]
[*]Let l be the larger number
[*]Let s be the smaller number
[/LIST]
We're given two equations:
[LIST=1]
[*]l = s + 4
[*]l + s = 40
[/LIST]
To get this problem in terms of the larger number l, we rearrange equation (1) in terms of l.
Subtract 4 from each side in equation (1)
l - 4 = s + 4 - 4
Cancel the 4's and we get:
s = l - 4
Our given equations are now:
[LIST=1]
[*]s = l - 4
[*]l + s = 40
[/LIST]
Substitute equation (1) into equation (2) for s:
l + l - 4 = 40
Grouping like terms for l, we get:
2l - 4 = 40
Add 4 to each side:
2l - 4 + 4 = 40 + 4
Cancelling the 4's on the left side, we get
2l = 44
Divide each side of the equation by 2 to isolate l:
2l/2 = 44/2
Cancel the 2's on the left side and we get:
l = [B]22[/B]

Length (l) is the same as width (w) and their product is 64.

Length (l) is the same as width (w) and their product is 64.
We're given 2 equations:
[LIST=1]
[*]lw = 64
[*]l = w
[/LIST]
Substitute equation (2) into equation (1):
w * w = 64
w^2 = 64
[B]w = 8[/B]
Since l = w, then [B]l = 8[/B]

Letter Arrangements in a Word

Given a word, this determines the number of unique arrangements of letters in the word.

Line Equation-Slope-Distance-Midpoint-Y intercept

Enter 2 points, and this calculates the following:

* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points

* Midpoint of the two points

* Distance between the 2 points

* 2 remaining angles of the rignt triangle formed by the 2 points

* y intercept of the line equation

* Point-Slope Form

* Parametric Equations and Symmetric Equations

Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.

Also allows for the entry of m and b to form the line equation

* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points

* Midpoint of the two points

* Distance between the 2 points

* 2 remaining angles of the rignt triangle formed by the 2 points

* y intercept of the line equation

* Point-Slope Form

* Parametric Equations and Symmetric Equations

Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.

Also allows for the entry of m and b to form the line equation

Linear Congruence

Given an modular equation ax ≡ b (mod m), this solves for x if a solution exists

Linear Conversions

Converts to and from the following linear measurements for a given quantity:

Inches

Feet

Yards

Miles

Micrometer

Millimeters

Centimeters

Meters

Kilometers

Furlongs

Inches

Feet

Yards

Miles

Micrometer

Millimeters

Centimeters

Meters

Kilometers

Furlongs

Littles Law

Given two out of the three inputs for Littles Law, Throughput (TH), Cycle Time (CT, and WIP, this solves for the third item.

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]

Logistic Map

Given r, x_{0} and (n) trials, this will display the logistic map.

Lois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity pay

Lois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity payment made on the date of purchase. What is the value of the annuity on the purchase date given a discount rate of 7 percent?
This is an annuity due, since the first payment is made on the date of purchase.
Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=5000&n=20&i=7&check1=2&pl=Calculate']present value of an annuity due calculator[/URL], we get [B]56,677.98[/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]

Lotto Drawing Probability

Given a lotto drawing with a Pick(x) out of (y) total choices, this calculates the probability of winning that lottery picking all (x) correct numbers.

Luke and Dan's total debt is $72. If Luke's debt is three times Dan's debt, what is Dan's debt?

Luke and Dan's total debt is $72. If Luke's debt is three times Dan's debt, what is Dan's debt?
Let Dan's debt be d.
Let Luke's debt be l.
We're given two equations:
[LIST=1]
[*]d + l = 72
[*]l = 3d
[/LIST]
Substitute equation (2) for l into equation (1):
d + 3d = 72
Solve for [I]d[/I] in the equation d + 3d = 72
[SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE]
(1 + 3)d = 4d
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
4d = + 72
[SIZE=5][B]Step 3: Divide each side of the equation by 4[/B][/SIZE]
4d/4 = 72/4
d = [B]18[/B]

M is the midpoint of AB. Prove AB=2AM

M is the midpoint of AB. Prove AB=2AM
M is the midpoint of AB (Given)
AM = MB (Definition of Congruent Segments)
AM + MB = AB (Segment Addition Postulate)
AM + AM = AB (Substitution Property of Equality)
2AM = AB (Distributive property)

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]

MAPE - MPE - MAPD

Given a time series of actual and forecasted values, this determines the following:

* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)

* Symmetric Mean Absolute Percentage Error (sMAPE)

* Mean Absolute Percentage Error (MPE)

* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)

* Symmetric Mean Absolute Percentage Error (sMAPE)

* Mean Absolute Percentage Error (MPE)

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]

Margin of Error from Confidence Interval

Given a confidence interval, this determines the margin of error and sample mean.

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]

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]

Markov Chain

Given a transition matrix and initial state vector, this runs a Markov Chain process.

Markup Markdown

Given the 3 items of a markup word problem, cost, markup percentage, and sale price, this solves for any one of the three given two of the items. This works as a markup calculator, markdown calculator.

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]

Matrix Properties

Given a matrix |A|, this calculates the following items if they exist:

* Determinant = det(A)

* Inverse = A^{-1}

* Transpose = A^{T}

* Adjoint = adj(A)

* Eigen equation (characteristic polynomial) = det|λI - A|

* Trace = tr(A)

* Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form

* Dimensions of |A| m x n

* Order of a matrix

* Euclidean Norm ||A||

* Magic Sum if it exists

* Determines if |A| is an Exchange Matrix

* Determinant = det(A)

* Inverse = A

* Transpose = A

* Adjoint = adj(A)

* Eigen equation (characteristic polynomial) = det|λI - A|

* Trace = tr(A)

* Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form

* Dimensions of |A| m x n

* Order of a matrix

* Euclidean Norm ||A||

* Magic Sum if it exists

* Determines if |A| is an Exchange Matrix

Max and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00 bob bought 3 burgers and

Max and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00. Bob bought 3 burgers and 1 drink for $5.50. How much is each burger and drink?
[U]Set up the givens where b is the cost of a burger and d is the cost of a drink:[/U]
Max: 2b + 2d = 5
Bob: 3b + d = 5.50
[U]Rearrange Bob's equation by subtracting 3b from each side[/U]
(3) d = 5.50 - 3b
[U]Now substitute that d equation back into Max's Equation[/U]
2b + 2(5.50 - 3b) = 5
2b + 11 - 6b = 5
[U]Combine b terms:[/U]
-4b + 11 = 5
[U]Subtract 11 from each side[/U]
-4b = -6
[U]Divide each side by -4[/U]
b = 3/2
[B]b = $1.50[/B]
[U]Now plug that back into equation (3):[/U]
d = 5.50 - 3(1.50)
d = 5.50 - 4.50
[B]d = $1.00[/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]

Mcnemar Test

Given a 2 x 2 contingency table and a significance level, this will determine the test statistic, critical value, and hypothesis conclusion using a Mcnemar test.

Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she c

Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she charges $53 for each lawn, how many lawns must she service to make a profit of at $800 a month?
Melissa has a fixed cost of $264 per month in fuel. No variable cost is given. Our cost function is:
C(x) = Fixed Cost + Variable Cost. With variable cost of 0, we have:
C(x) = 264
The revenue per lawn is 53. So R(x) = 53x where x is the number of lawns.
Now, profit is Revenue - Cost. Our profit function is:
P(x) = 53x - 264
To make a profit of $800 per month, we set P(x) = 800.
53x - 264 = 800
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=53x-264%3D800&pl=Solve']equation solver[/URL], we get:
[B]x ~ 21 lawns[/B]

Method of Equated Time-Exact Method-Macaulay Duration-Volatility

Given a set of cash flows at certain times, and a discount rate, this will calculate t using the equated time method and the exact method, as well as the macaulay duration and volatility

Midpoint formula

Midpoint formula
Given two points (x1, y1) and (x2, y2), the midpoint is found as the average distance between the 2 points:
[LIST]
[*]x value is: (x1 + x2)/2
[*]y value is: (y1 + y2)/2
[/LIST]
So our midpoint is:
((x1 + x2)/2, (y1 + y2)/2)

Mindy and troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake troy had 1/4 of

Mindy and troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake troy had 1/4 of the total cake. Write an equation to determine how many pieces of cake (c) that were in total
Let c be the total number of pieces of cake. Let m be the number of pieces Mindy ate. Let t be the number of pieces Troy ate. We have the following given equations:
[LIST]
[*]m + t = 9
[*]m = 3
[*]t = 1/4c
[/LIST]
Combining (2) and (3) into (1), we have:
3 + 1/4c = 9
Subtract 3 from each side:
1/4c = 6
Cross multiply:
[B]c = 24[/B]

Missing Average

Given a set of scores and an average, this calculates the next score necessary to attain that average

Modified Internal Rate of Return (MIRR)

Given a set of positive/negative cash flows, a finance rate, and a reinvestment rate, this calculates the modified internal rate of return

Modified Payback Period

Given a set of cash inflows, outflows, and a discount rate, this calculates the modified payback period.

Modulus

Given 2 integers a and b, this modulo calculator determines a mod b or simplifies modular arithmetic such as 7 mod 3 + 5 mod 8 - 32 mod 5

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.

Money Multiplier

Given a reserve ratio and initial deposit amount, this calculates the money multiplier and displays the re-lending process table for a bank to other banks including reserves and loans.

Morse Code Translator

Given a phrase with letters, numbers, and most punctuation symbols, the calculator will perform the following duties:

1) Translate that phrase to Morse Code.

2) Translate the Morse Code to a Dit-Dah message

3) Calculate the number of dots in the message

4) Calculate the number of dashes in the message

This also translates__from__ Morse Code back to English.

1) Translate that phrase to Morse Code.

2) Translate the Morse Code to a Dit-Dah message

3) Calculate the number of dots in the message

4) Calculate the number of dashes in the message

This also translates

Mortgage

Calculates the monthly payment, APY%, total value of payments, principal/interest/balance at a given time as well as an amortization table on a __standard__ or __interest only__ home or car loan with fixed interest rate. Handles amortized loans.

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. Tan has two daughters. His elder daughter is 1/3 of his age while his younger daughter is 1/4 of

Mr. Tan has two daughters. His elder daughter is 1/3 of his age while his younger daughter is 1/4 of his age. If Mr. Tan’s age is 60, how old are his elder and youngest daughter?
Let Mr. Tan's age be a. We're given:
[LIST]
[*]Elder Daughter's age = 60/3 = [B]20 years old[/B]
[*]Younger Daughter's age = 60/4 = [B]15 years old[/B]
[/LIST]

Ms. Jeffers is splitting $975 among her three sons. If the oldest gets twice as much as the youngest

Ms. Jeffers is splitting $975 among her three sons. If the oldest gets twice as much as the youngest and the middle son gets $35 more than the youngest, how much does each boy get?
Let 0 be the oldest son, m be the middle sun, and y be the youngest son. Set up our given equations
[LIST]
[*]o = 2y
[*]m = y + 35
[*]o + m + y = 975
[/LIST]
[U]Substitute the first and second equations into Equation 3[/U]
2y + y + 35 + y = 975
[U]Combine the y terms[/U]
4y + 35 = 975
Subtract 35 using our [URL='http://www.mathcelebrity.com/1unk.php?num=4y%2B35%3D975&pl=Solve']equation calculator[/URL] to solve and get [B]y = 235[/B]
[U]Plug y = 235 into equation 2[/U]
m = 235 + 35
[B]m = 270[/B]
[U]Plug y = 235 into equation 2[/U]
o = 2(235)
[B]o = 470[/B]

Multinomial Distribution

Given a set of x_{i} counts and a respective set of probabilities θ_{i}, this calculates the probability of those events occurring.

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 is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daug

Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daughter?
Declare variables for each age:
[LIST]
[*]Let Nancy's age be n
[*]Let her daughter's age be d
[/LIST]
We're given two equations:
[LIST=1]
[*]n = 3d - 10
[*]n = 41
[/LIST]
We set 3d - 10 = 41 and solve for d:
Solve for [I]d[/I] in the equation 3d - 10 = 41
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants -10 and 41. To do that, we add 10 to both sides
3d - 10 + 10 = 41 + 10
[SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE]
3d = 51
[SIZE=5][B]Step 3: Divide each side of the equation by 3[/B][/SIZE]
3d/3 = 51/3
d = [B]17[/B]

Net Present Value (NPV) - Internal Rate of Return (IRR) - Profitability Index

Given a series of cash flows C_{t} at times t and a discount rate of (i), the calculator will determine the Net Present Value (NPV) at time 0, also known as the discounted cash flow model.

Profitability Index

Also determines an Internal Rate of Return (IRR) based on a series of cash flows. NPV Calculator

Profitability Index

Also determines an Internal Rate of Return (IRR) based on a series of cash flows. NPV Calculator

Nick is given $50 to spend on a vacation . He decides to spend $5 a day. Write an equation that show

Nick is given $50 to spend on a vacation . He decides to spend $5 a day. Write an equation that shows how much money Nick has after x amount of days.
Set up the function M(x) where M(x) is the amount of money after x days. Since spending means a decrease, we subtract to get:
[B]M(x) = 50 - 5x[/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]

Nine workers are hired to harvest potatoes from a field. Each is given a plot which is 5x5 feet in s

Nine workers are hired to harvest potatoes from a field. Each is given a plot which is 5x5 feet in size. What is the total area of the field?
Area of each plot is 5x5 = 25 square feet.
Total area = Area per plot * number of plots
Total area = 25 sq ft * 9
Total area = [B]225 sq ft[/B]

Nominal Yield

Given an effective annual rate of interest based on a compounding period, this determines the nominal yield.

Number Line Midpoint

Calculates a midpoint between 2 points on a number line or finds the second endpoint if one endpoint and midpoint are given.

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]

Odds Probability

Given an odds prediction m:n of an event success, this calculates the probability that the event will occur or *not* occur

Of all smokers in particular district, 40% prefer brand A and 60% prefer brand B. Of those who prefe

Of all smokers in particular district, 40% prefer brand A and 60% prefer brand B. Of those who prefer brand A, 30% are female, and of those who prefer brand B, 40% are female.
Q: What is the probability that a randomly selected smoker prefers brand A, given that the person selected is a female?
P(F) = P(F|A)*P(A) + P(F|B)*P(B)
P(F) = 0.3*0.4 + 0.4*0.6 = 0.36
So, 36% of all the smokers are female.
You are looking for P(A|F)
P(A|F) = P(A and F)/P(F)
P(A|F) = (P(F|A)*P(A))/P(F)
P(A|F) = (0.3 * 0.4)/0.36
P(A|F) = [B]0.33 or 33%[/B]

On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two

On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two grades was 138. Find the lowest grade.
[U]Let h be the highest grade and l be the lowest grade. Set up the given equations:[/U]
(1) h = l + 42
(2) h + l = 138
[U]Substitute (1) into (2)[/U]
l + 42 + l = 138
[U]Combine l terms[/U]
2l + 42 = 138
[U]Enter that equation into our [URL='http://www.mathcelebrity.com/1unk.php?num=2l%2B42%3D138&pl=Solve']equation calculator[/URL] to get[/U]
[B]l = 48
[/B]
[U]Substitute l = 48 into (1)[/U]
h = 48 + 42
[B]h = 90[/B]

On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday

On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday they paid 15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel
Let the number of cups of coffee be c
Let the number of bagels be b.
Since cost = Price * Quantity, we're given two equations:
[LIST=1]
[*]7b + 4c = 8.77
[*]14b + 8c = 15.80
[/LIST]
We have a system of equations. We can solve this 3 ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer
[LIST]
[*]The system is inconsistent. Therefore, we have no answer.
[/LIST]

On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a

On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a total of $82. The school took in $67 on the second day by selling 8 senior citizen tickets And 5 child tickets. What is the price of each ticket?
Let the number of child tickets be c
Let the number of senior citizen tickets be s
We're given two equations:
[LIST=1]
[*]10c + 3s = 82
[*]5c + 8s = 67
[/LIST]
We have a system of simultaneous equations. We can solve it using any one of 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]c = 7[/B]
[*][B]s = 4[/B]
[/LIST]

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]

Opposite Numbers

Given a positive or negative integer (n), this calculates the opposite number of n

Ordered and Unordered Partitions

Given a population size (n) and a group population of (m), this calculator determines how many ordered or unordered groups of (m) can be formed from (n)

Ordering Numbers

Given a list of numbers, this will order the list ascending (lowest to highest or least to greatest) or descending (highest to lowest or greatest to least)

P-Hat Confidence Interval

Given a large sized distribution, and a success amount for a certain criteria x, and a confidence percentage, this will calculate the confidence interval for that criteria.

Pam has two part-time jobs. At one job, she works as a cashier and makes $8 per hour. At the second

Pam has two part-time jobs. At one job, she works as a cashier and makes $8 per hour. At the second job, she works as a tutor and makes$12 per hour. One week she worked 30 hours and made$268 . How many hours did she spend at each job?
Let the cashier hours be c. Let the tutor hours be t. We're given 2 equations:
[LIST=1]
[*]c + t = 30
[*]8c + 12t = 268
[/LIST]
To solve this system of equations, we can use 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+30&term2=8c+%2B+12t+%3D+268&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+30&term2=8c+%2B+12t+%3D+268&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+30&term2=8c+%2B+12t+%3D+268&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*]c = [B]23[/B]
[*]t = [B]7[/B]
[/LIST]

Parallel Resistors

Given a set of parallel resistors, this calculates the total resistance in ohms, denoted R_{t}

Payback Period

Given a set of cash inflows and cash outflows at certain times, this determines the net cash flow, cumulative cash flow, and payback period

Pentagons

Given a side length and an apothem, this calculates the perimeter and area of the pentagon.

Percent Off Problem

Given the 3 items of a percent word problem, Reduced Price, percent off, and full price, this solves for any one of the three given two of the items.

Percentage Appreciation

Solves for Book Value given a flat rate percentage appreciation per period

Percentage Depreciation

Solves for Book Value given a flat rate percentage depreciation per period

Percentage of Completion

Given a sales price, total costs, and costs per period, this determines the gross profit to date using the percentage of completion method.

Percentile for Normal Distribution

Given a mean, standard deviation, and a percentile range, this will calculate the percentile value.

Percentiles

Given a set of scores and a target score, this will determine the percentile of the target score using two different formulas.

Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width?

Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width?
The perimeter P of a rectangle with length l and width w is:
2l + 2w = P
We're given P = 372 and l = 99, so we have:
2(99) + 2w = 372
2w + 198 = 372
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 198 and 372. To do that, we subtract 198 from both sides
2w + 198 - 198 = 372 - 198
[SIZE=5][B]Step 2: Cancel 198 on the left side:[/B][/SIZE]
2w = 174
[SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE]
2w/2 = 174/2
w = [B]87[/B]

Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he

Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?
Let the cost of paper packages be p and the cost of staplers be s. We're given two equations:
[LIST=1]
[*]3p + 4s = 40
[*]5p + 6s = 62
[/LIST]
We have a system of equations. We can solve this three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get the same answer:
[LIST]
[*][B]p = 4[/B]
[*][B]s = 7[/B]
[/LIST]

Phone Number Translator

Given a phone number with letters in it, this calculator will determine the numeric phone number for you to dial.

Phonetic Algorithms

Given a name, this calculator translates a name to one of the following 3 phonetic algorithms:

* Soundex

* Metaphone

* New York State Identification and Intelligence System (NYSIIS)

* Soundex

* Metaphone

* New York State Identification and Intelligence System (NYSIIS)

Place Value

Given a whole number or a decimal, the calculator will perform place number analysis on each place in your number.

For the whole and decimal portion, the calculator goes out to the 100 trillion mark.

For the whole and decimal portion, the calculator goes out to the 100 trillion mark.

Plane and Parametric Equations in R

Given a vector A and a point (x,y,z), this will calculate the following items:

1) Plane Equation passing through (x,y,z) perpendicular to A

2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A

1) Plane Equation passing through (x,y,z) perpendicular to A

2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A

Point Estimate and Margin of Error

Given an upper bound and a lower bound and a sample size, this calculate the point estimate, margin of error.

Polar Conics

Given eccentricity (e), directrix (d), and angle θ, this determines the vertical and horizontal directrix polar equations.

Polygon Side

Determines the sides of a polygon given an interior angle sum.

Pool Volume

Given a round shaped pool, this calculates the volume (Capacity) in gallons of the pool when filled with water

Portfolio Rate of Return

Given a portfolio of individual assets with returns and weights, this calculates the total portfolio rate of return.

Power Sets and Set Partitions

Given a set S, this calculator will determine the power set for S and all the partitions of a set.

Predecessor

Calculates the predecessor number to a given number

Price

Given a cost and a gross margin percentage, this calculator calculates price, gross profit, markup percentage

Primitive Root

Given a prime number p and a potential root of b, this determines if b is a primitive root of p.

Probability (A U B)

Given a 2 event sample space A and B, this calculates the probability of the following events:

P(A U B)

P(A)

P(B)

P(A ∩ B)

P(A U B)

P(A)

P(B)

P(A ∩ B)

Problems Involving Rational Expressions

We are given, using the word word problem combined formula, that:
1/j + 1/p + 1/m = 1/3
However, you state the hours working alone, but then ask how much it would take working alone. I'm confused on the last part. Can you clarify?

Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR?

Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR?
From segment addition, we know that:
PQ + QR = PR
Plugging our given numbers in, we get:
2.7 + QR = 6.1
Subtract 2.7 from each side, and we get:
2.7 - 2.7 + QR = 6.1 - 2.7
Cancelling the 2.7 on the left side, we get:
QR = [B]3.4[/B]

Quadrilateral

Given 4 points entered, this determines the area using Brahmaguptas Formula and perimeter of the quadrilateral formed by the points as well as checking to see if the quadrilateral (quadrangle) is a parallelogram.

Quotient-Remainder Theorem

Given 2 positive integers n and d, this displays the quotient remainder theorem.

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]

Random Test

Given a set of data and an α value, this determines the test statistic and accept/reject hypothesis based on randomness of a dataset.

Rates of Return

Given a set of stock prices and dividends if applicable, this calculates the periodic rate of return and the logarithmic rate of return

Ratio Word Problems

Solves a ratio word problem using a given ratio of 2 items in proportion to a whole number.

Ratios

* Simplifies a ratio of a:b

* Given a ratio in the form a:b or a to b, and a total population amount, this calculator will determine the expected value of A and B from the ratio.

* Given a ratio in the form a:b or a to b, and a total population amount, this calculator will determine the expected value of A and B from the ratio.

Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much inte

Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will he be paid in the first 4 years?
The formula for [U]interest[/U] using simple interest is:
I = Prt where P = Principal, r = interest, and t = time.
We're given P = 500, r =0.04, and t = 4. So we plug this in and get:
I = 500(0.04)(4)
I = [B]80[/B]

Rebound Ratio

Calculates a total downward distance traveled given an initial height of a drop and a rebound ratio percentage

Receivables Ratios

Given Net Sales, Beginning Accounts Receivable, and Ending Accounts Receivable, this determines Average Accounts Receivable, Receivables turnover ratio, and Average Collection Period.

rectangle abcd prove: triangle adc is congruent to triangle bcd

rectangle abcd prove: triangle adc is congruent to triangle bcd
1. Given: ABCD is a rectangle
2. AB = CD since opposite sides of rectangle are congruent
3. BC = AD since opposite sides of rectangle are congruent
4. AC = AC by the Reflexive Property of Equality
5. triangle ADC = triangle CBA by the Side-Side-Side (SSS) Property

Reference Angle

Calculates the reference angle for a given angle. Also known as the positive acute angle.

Relative Coordinates

Given a starting point (x_{1},y_{1}), this will determine your relative coordinates after moving up, down, left, and right.

Resistor Color Codes

Given 3 Band level color codes and a tolerance color chosen, this calculates the resistance in ohms and the tolerance percentage

Rhombus

Given inputs of a rhombus, this calculates the following:

Perimeter of a Rhombus

Area of a Rhombus

Side of a Rhombus

Perimeter of a Rhombus

Area of a Rhombus

Side of a Rhombus

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]

Right Triangles

This solves for all the pieces of a right triangle based on given inputs using items like the sin ratio, cosine ratio, tangent ratio, and the Pythagorean Theorem as well as the inradius.

Roster Notation

Given a set of numbers, this displays the roster notation

Rule of Succession

Given s successes in n independent trials, this calculates the probability that the next repetition is a success

Run Length Encoding

Given a string, this will determine the run length encoding using repeating patterns of characters.

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

Given a sales price and a total bill, this calculates the sales tax amount and sales tax percentage

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 earns $19.25 per hour. This week she earned $616. Write a two step equation to represent the p

Sally earns $19.25 per hour. This week she earned $616. Write a two step equation to represent the problem
Let hours be h. We're given:
[B]19.25h = 616[/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 has $2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how

Sam has $2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how many dimes?
Let d be the number of dimes. Let q be the number of quarters. We're given two equations:
[LIST=1]
[*]0.1d + 0.25q = 2.25
[*]d + q = 12
[/LIST]
We have a simultaneous system of equations. We can solve this 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]d = 5[/B]
[*][B]q = 7[/B]
[/LIST]

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]

Sample Size Reliability for μ

Given a population standard deviation σ, a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.

Sample Size Requirement for the Difference of Means

Given a population standard deviation 1 of σ_{1}, a population standard deviation 2 of σ_{2} a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.

Sample Space Probability

Given a sample space S and an Event Set E, this calculates the probability of the event set occuring.

Sequences

Given a function a(n) and a count of sequential terms you want to expand (n), this calcuator will determine the first (n) terms of your sequence, {a_{1}, a_{2}, ..., a_{n}}

Set Notation

Given two number sets A and B, this determines the following:

* Union of A and B, denoted A U B

* Intersection of A and B, denoted A ∩ B

* Elements in A not in B, denoted A - B

* Elements in B not in A, denoted B - A

* Symmetric Difference A Δ B

* The Concatenation A · B

* The Cartesian Product A x B

* Cardinality of A = |A|

* Cardinality of B = |B|

* Jaccard Index J(A,B)

* Jaccard Distance J_{σ}(A,B)

* Dice's Coefficient

* If A is a subset of B

* If B is a subset of A

* Union of A and B, denoted A U B

* Intersection of A and B, denoted A ∩ B

* Elements in A not in B, denoted A - B

* Elements in B not in A, denoted B - A

* Symmetric Difference A Δ B

* The Concatenation A · B

* The Cartesian Product A x B

* Cardinality of A = |A|

* Cardinality of B = |B|

* Jaccard Index J(A,B)

* Jaccard Distance J

* Dice's Coefficient

* If A is a subset of B

* If B is a subset of A

Set of 2 digit even numbers less than 40

Set of 2 digit even numbers less than 40
Knowns and givens:
[LIST]
[*]2 digit numbers start at 10
[*]Less than 40 means we do not include 40
[*]Even numbers are divisible by 2
[/LIST]
[B]{10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38}[/B]

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself how many

Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself how many plums did she have at first?
Let p be the number of plums Shalini started with. We have:
[LIST]
[*]0.4 given to her brother
[*]20% which is 0.2 given away to her sister
[*]What this means is she kept 1 - (0.4 + 0.2) = 1 - 0.6 = 0.4 for herself
[/LIST]
0.4p = 16
Divide each side by 0.4
[B]p = 40[/B]

Sharpe Ratio

Calculates the Sharpe ratio given return on assets, risk free rate, and standard deviation

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]

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]

Sigmoid Function

Calculates the Sigmoid Function S(x) given an x value

Simple Discount and Compound Discount

Given a principal value, interest rate, and time, this calculates the Accumulated Value using Simple Discount and Compound Discount

Sine Wave

Solves for any of the 3 items of the Sine Wave: Peak Value, Average Value, and RMS value given 1 input.

Small pizzas were $3 and large pizzas were $5. To feed the throng, it was necessary to spend $475 fo

Small pizzas were $3 and large pizzas were $5. To feed the throng, it was necessary to spend $475 for 125 pizzas. How many small pizzas were purchased?
Let s be the number of small pizzas and l be the number of large pizzas. We have two given equations:
[LIST=1]
[*]l + s = 125
[*]3s + 5l = 475
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+s+%3D+125&term2=3s+%2B+5l+%3D+475&pl=Cramers+Method']simultaneous equation calculator[/URL], we get [B]s = 75[/B]:

Solution Mixture

Determines a necessary amount of a Solution given two solution percentages and 1 solution amount.

Some History teachers at Richmond High School are purchasing tickets for students and their adult ch

Some History teachers at Richmond High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Yang bought 30 student tickets and 30 adult tickets, which cost a total of $750. Mr. Alexander spent $682, getting 28 student tickets and 27 adult tickets. What is the price for each type of ticket?
Let the number of adult tickets be a
Let the number of student tickets be s
We're given two equations:
[LIST=1]
[*]30a + 30s = 750
[*]27a + 28s = 682
[/LIST]
To solve the simultaneous equations, we can use any of three methods below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we use, we get the same answers:
[LIST]
[*][B]a = 18[/B]
[*][B]s = 7[/B]
[/LIST]

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is runn

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is running at 5 feet per second and Claire is running at 3 feet per second.
i. After how many seconds will Sophie catch Claire?
ii. If the race is 500 feet, who wins?
i.
Sophie's distance formula is given as D = 5s
Claire's distance formula is given as D = 3s + 100
Set them equal to each other
5s = 3s + 100
Subtract 3s from both sides:
2s = 100
Divide each side by 2
[B]s = 50[/B]
ii. [B]Sophie since after 50 seconds, she takes the lead and never gives it back.[/B]

Special Triangles: Isosceles and 30-60-90

Given an Isosceles triangle (45-45-90) or 30-60-90 right triangle, the calculator will solve the 2 remaining sides of the triangle given one side entered.

spent $19.05. ended with $7.45. how much did you start with?

spent $19.05. ended with $7.45. how much did you start with?
Let s be the amount we started with. We're given:
s - 19.05 = 7.45
To solve this equation for s, we t[URL='https://www.mathcelebrity.com/1unk.php?num=s-19.05%3D7.45&pl=Solve']ype it in our math engine [/URL]and we get:
[B]s = 26.5[/B]

Split Fund Interest

Given an initial principal amount, interest rate on Fund 1, interest rate on Fund 2, and a total interest paid, calculates the amount invested in each fund.

Square Roots and Exponents

Given a number (n), or a fraction (n/m), and/or an exponent (x), or product of up to 5 radicals, this determines the following:

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x^{th} power denoted as n^{x} (Write without exponents)

* n raised to the x^{th} power raised to the yth power denoted as (n^{x})^{y} (Write without exponents)

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x

* n raised to the x

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

Standard Normal Distribution

Givena normal distribution z-score critical value, this will generate the probability. Uses the NORMSDIST Excel function.

Stanley bought a ruler and a yardstick for $1.25. If the yardstick cost 45 cents more than the ruler

Stanley bought a ruler and a yardstick for $1.25. If the yardstick cost 45 cents more than the ruler, what was the cost of the yardstick?
Let r be the cost of the ruler
Let y be the cost of the yardstick
We're given 2 equations:
[LIST=1]
[*]r + y = 1.25
[*]y = r + 0.45
[/LIST]
Substitute equation (2) into equation (1) for y
r + r + 0.45 = 1.25
Solve for [I]r[/I] in the equation r + r + 0.45 = 1.25
[SIZE=5][B]Step 1: Group the r terms on the left hand side:[/B][/SIZE]
(1 + 1)r = 2r
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
2r + 0.45 = + 1.25
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 0.45 and 1.25. To do that, we subtract 0.45 from both sides
2r + 0.45 - 0.45 = 1.25 - 0.45
[SIZE=5][B]Step 4: Cancel 0.45 on the left side:[/B][/SIZE]
2r = 0.8
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2r/2 = 0.8/2
r = 0.4
Substitute r = 0.4 into equation (2) above:
y = r + 0.45
y = 0.4 + 0.45
r = [B]0.85
[URL='https://www.mathcelebrity.com/1unk.php?num=r%2Br%2B0.45%3D1.25&pl=Solve']Source[/URL][/B]

Static Determinacy and Stability

Given a number of joints (j) and a number of members (m), this determines if a truss is statically determinate, statically indeterminate, or unstable

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]

Stopping-Braking Distance for a Car

Calculates the estimated stopping distance of a vehicle given a speed in miles per hour (mph)

String Comparison Algorithms

Given two strings A and B, this calculates the following items:

1) Similar Text Pair Ranking Score

2) Levenshtein (Edit Distance).

1) Similar Text Pair Ranking Score

2) Levenshtein (Edit Distance).

Student-t Distribution Critical Values

Given an α value and degrees of freedom, this calculates the right-tailed test and left-tailed test critical values for the Student-t Distribution

Substitute the given values into given formula and solve for the unknown variable. S=4LW + 2 WH; S=

Substitute the given values into given formula and solve for the unknown variable. S = 4LW + 2 WH; S= 144, L= 8, W= 4. H=
S = 4LW + 2 WH
Substituting our given values, we have:
144 = 4(8)(4) + 2(4)H
144 = 128 + 8H
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=128%2B8h%3D144&pl=Solve']equation calculator[/URL], we get:
[B]H = 2[/B]

Successor

Calculates the successor number to a given number

Sum to Product and Product to Sum Formulas

Given two angles in degrees of u and v, this determines the following:

* Sin(u) ± Sin(v)

* Cos(u) ± Cos(v)

* Sin(u)Sin(v)

* Cos(u)Cos(v)

* Sin(u)Cos(v)

* Cos(u)Sin(v)

* Sin(u + v)

* Sin(u - v)

* Cos(u + v)

* Cos(u - v)

* Tan(u + v)

* Tan(u - v)

* Sin(u) ± Sin(v)

* Cos(u) ± Cos(v)

* Sin(u)Sin(v)

* Cos(u)Cos(v)

* Sin(u)Cos(v)

* Cos(u)Sin(v)

* Sin(u + v)

* Sin(u - v)

* Cos(u + v)

* Cos(u - v)

* Tan(u + v)

* Tan(u - v)

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in ga

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 20 gallons of fuel, the airplane weighs 2012 pounds. When carrying 55 gallons of fuel, it weighs 2208 pounds. How much does the airplane weigh if it is carrying 65 gallons of fuel?
Linear functions are written in the form of one dependent variable and one independent variable. Using g as the number of gallons and W(g) as the weight, we have:
W(g) = gx + c where c is a constant
We are given:
[LIST]
[*]W(20) = 2012
[*]W(55) = 2208
[/LIST]
We want to know W(65)
Using our givens, we have:
W(20) = 20x + c = 2012
W(55) = 55x + c = 2208
Rearranging both equations, we have:
c = 2012 - 20x
c = 2208 - 55x
Set them both equal to each other:
2012 - 20x = 2208 - 55x
Add 55x to each side:
35x + 2012 = 2208
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=35x%2B2012%3D2208&pl=Solve']equation solver[/URL], we see that x is 5.6
Plugging x = 5.6 back into the first equation, we get:
c = 2012 - 20(5.6)
c = 2012 - 112
c = 2900
Now that we have all our pieces, find W(65)
W(65) = 65(5.6) + 2900
W(65) = 264 + 2900
W(65) = [B]3264[/B]

Survival Rates

Given a set of times and survival population counts, the calculator will determine the following:

Survival Population l_{x}

Mortality Population d_{x}

Survival Probability p_{x}

Mortality Probability q_{x}

In addition, the calculator will determine the probability of survival from t_{x} to t_{x + n}

Survival Population l

Mortality Population d

Survival Probability p

Mortality Probability q

In addition, the calculator will determine the probability of survival from t

Susan works as a tutor for $14 an hour and as a waitress for $13 an hour. This month, she worked a c

Susan works as a tutor for $14 an hour and as a waitress for $13 an hour. This month, she worked a combined total of 104 hours at her two jobs. Let t be the number of hours Susan worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.
Let t be the number of hours for math tutoring and w be the number of hours for waitressing. We're given:
[LIST=1]
[*]t + w = 104
[*]14t + 13w = D <-- Combined total dollar amount
[/LIST]

tammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 total

tammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 total
We have a commission equation below:
Sales * Commission percent = Salary
We're given 4% commission percent and 55,000 salary. With 4% as 0.04, we have:
Sales * 0.04 = 55,000
Divide each side of the equation by 0.04, and we get:
Sales = [B]1,375,000[/B]

Target Heart Rate

Given an age, this calculator determines the following 5 target heart rate zones:

Healthy Heart Zone (Warm up) 50 - 60%

Fitness Zone (Fat Burning) 60 - 70%

Aerobic Zone (Endurance Training) 70 - 80%

Anaerobic Zone (Performance Training) 80 - 90%

Red Line (Maximum Effort) 90 - 100%

Healthy Heart Zone (Warm up) 50 - 60%

Fitness Zone (Fat Burning) 60 - 70%

Aerobic Zone (Endurance Training) 70 - 80%

Anaerobic Zone (Performance Training) 80 - 90%

Red Line (Maximum Effort) 90 - 100%

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 32

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 327 people entered the park , and the admission fee collected totaled 978.00 dollars . How many children and how many adults were admitted?
Let the number of children's tickets be c. Let the number of adult tickets be a. We're given two equations:
[LIST=1]
[*]a + c = 327
[*]4a + 1.50c = 978
[/LIST]
We can solve this system of equation 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answers:
[LIST]
[*][B]a = 195[/B]
[*][B]c = 132[/B]
[/LIST]

The average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the numbe

The average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the number of books printed that day and k is a constant. Find k, if on the day when 200 were printed the average cost was $9 per book.
We are given: c(200) = 9, so we have:
9 = 5.5(200) + k(200)
200k + 1100 = 9
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=200k%2B1100%3D9&pl=Solve']equation solver[/URL], we get:
[B]k = -5.455[/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 base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of th

The base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of the triangle is less than 10 units. Write and solve an inequality that represents the possible area A of the triangle
We're given:
b=2/7A
We're also told that b is less than 10. So we have:
2/7A < 10
2A/7 < 10
Cross multiply:
2A < 7 * 10
2A < 70
Divide each side of the inequality by 2 to isolate A
2A/2 < 70/2
Cancel the 2's on the left side and we get:
A < [B]35[/B]

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 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 buffet at a restaurant is different for adults and kids. the bill for 2 adults and 3 k

the cost of a buffet at a restaurant is different for adults and kids. the bill for 2 adults and 3 kids is $51. the bill for 3 adults and 1 kid is $45. what is the cost per adult and per kid?
Let the cost for each adult be a
Let the cost for each kid be k
We're given two equations:
[LIST=1]
[*]2a + 3k = 51
[*]3a + k = 45
[/LIST]
To solve this simultaneous set of equations, we can use three methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2a+%2B+3k+%3D+51&term2=3a+%2B+k+%3D+45&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2a+%2B+3k+%3D+51&term2=3a+%2B+k+%3D+45&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2a+%2B+3k+%3D+51&term2=3a+%2B+k+%3D+45&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*]a = [B]12[/B]
[*]k = [B]9[/B]
[/LIST]

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 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 numbers is 96. One number is 9 times the other. What are the numbers?

The difference between two numbers is 96. One number is 9 times the other. What are the numbers?
Let x be the first number
Let y be the second number
We're given two equations:
[LIST=1]
[*]x - y = 96
[*]x = 9y
[/LIST]
Substitute equation (2) into equation (1) for x
9y - y = 96
[URL='https://www.mathcelebrity.com/1unk.php?num=9y-y%3D96&pl=Solve']Plugging this equation into our math engine[/URL], we get:
y = [B]12
[/B]
If y = 12, then we plug this into equation 2:
x = 9(12)
x = [B]108[/B]

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 first group orders 3 pizzas and 4 drinks for $33.50. The second group orders 5 pizzas and 6 drin

The first group orders 3 pizzas and 4 drinks for $33.50. The second group orders 5 pizzas and 6 drinks for $54. Find the cost for each pizza and each drink
Assumptions:
[LIST]
[*]Let the cost of each pizza be p
[*]Let the cost of each drink be d
[/LIST]
Givens:
[LIST=1]
[*]4d + 3p = 33.50
[*]6d + 5p = 54
[/LIST]
We have a simultaneous group of equations. To solve this, we can use 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+3p+%3D+33.50&term2=6d+%2B+5p+%3D+54&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+3p+%3D+33.50&term2=6d+%2B+5p+%3D+54&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+3p+%3D+33.50&term2=6d+%2B+5p+%3D+54&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we use, we get the same answer:
[LIST]
[*]d = [B]$2.75[/B]
[*]p = [B]$7.5[/B]
[/LIST]

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 Lakers recently scored 81 points. Their points came from 2 and 3 point baskets. If they made 39

The Lakers recently scored 81 points. Their points came from 2 and 3 point baskets. If they made 39 baskets total, how many of each basket did they make?
Let x = 2 point baskets and y = 3 point baskets. We have the following given equations:
[LIST=1]
[*]x + y = 39
[*]2x + 3y = 81
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=x%2By%3D39&term2=2x+%2B+3y+%3D+81&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[B]x = 36 <-- 2 point baskets
y = 3 <-- 3[B] point baskets
[/B][/B]
To confirm our work:
[LIST=1]
[*]36 + 3 = 39
[*]2(36) + 3(3) = 72 + 9 = 81
[/LIST]

The Lakewood library has $8,040 to buy science magazines. If each magazine costs $3, how many magazi

The Lakewood library has $8,040 to buy science magazines. If each magazine costs $3, how many magazines will the library be able to buy?
Let number of magazines be m. We know that:
Cost per magazine * m = Total Cost
We're given Total Cost = 8040 and Cost per magazine = 3, so we have
3m = 8040
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%3D8040&pl=Solve']type it in our math engine[/URL] and we get:
m = [B]2680[/B]

The largest American flag ever flown had a perimeter of 1,520 feet and a length of 505 feet. Find th

The largest American flag ever flown had a perimeter of 1,520 feet and a length of 505 feet. Find the width of the flag.
for a rectangle, the Perimeter P is given by:
P = 2l + 2w
P[URL='https://www.mathcelebrity.com/rectangle.php?l=505&w=&a=&p=1520&pl=Calculate+Rectangle']lugging in our numbers for Perimeter and width into our rectangle calculator[/URL], we get:
l =[B] 255[/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 rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
P = 2l + 2w
Since P = 120, we have:
(1) 2l + 2w = 120
We are also given:
(2) l = 3w - 6
Substitute equation (2) into equation (1)
2(3w - 6) + 2w = 120
Multiply through:
6w - 12 + 2w = 120
Combine like terms:
8w - 12 = 120
Add 12 to each side:
8w = 132
Divide each side by 8 to isolate w:
w =16.5
Now substitute w into equation (2)
l = 3(16.5) - 6
l = 49.5 - 6
l = 43.5
So (l, w) = (43.5, 16.5)

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 12ft˛

The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft˛
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 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 12 scores is 8.8 . what is the sum of the scores ?

the mean of 12 scores is 8.8 . what is the sum of the scores ?
The Mean is denoted as:
Mean = Sum / count
We're given:
8.8 = Sum / 12
Cross multiply and we get:
Sum = 8.8*12
Sum = [B]105.6[/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 perimeter of a college basketball court is 102 meters and the length is twice as long as the wid

The perimeter of a college basketball court is 102 meters and the length is twice as long as the width. What are the length and width?
A basketball court is a rectangle. The perimeter P is:
P = 2l + 2w
We're also given l = 2w and P = 102. Plug these into the perimeter formula:
2(2w) + 2w = 102
4w + 2w = 102
6w = 102
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%3D102&pl=Solve']Typing this equation into our calculator[/URL], we get:
[B]w = 17[/B]
Plug this into the l = 2w formula, we get:
l = 2(17)
[B]l = 34[/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 rectangular bakery is 204 feet. It is 66 feet long. How wide is it?

The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it?
Set up the perimeter equation:
2l + 2w = P
Given P = 204 and l = 66, we have:
2(66) + 2w = 204
2w + 132 = 204
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B132%3D204&pl=Solve']equation solver,[/URL] we get w = [B]36[/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 notecard is 16 inches. The notecard is 5 inches wide. How tall is it?

The perimeter of a rectangular notecard is 16 inches. The notecard is 5 inches wide. How tall is it?
Perimeter of a rectangle P is:
P = 2l + 2w
We have:
2l + 2w = 16
We are given w = 5, so we have:
2l + 2(5) = 16
2l + 10 = 16
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B10%3D16&pl=Solve']Plugging this into our equation calculator[/URL], we get [B]l = 3[/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 Radio City Music Hall is selling tickets to Kayla’s premiere at the Rockettes. On the first day

The Radio City Music Hall is selling tickets to Kayla’s premiere at the Rockettes. On the first day of ticket sales they sold 3 senior citizen tickets and 9 child tickets for a total of $75. It took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of each senior citizen ticket and each child ticket?
Let the cost of child tickets be c
Let the cost of senior tickets be s
Since revenue = cost * quantity, we're given two equations:
[LIST=1]
[*]9c + 3s = 75
[*]5c + 8s = 67
[/LIST]
To solve this simultaneous group of equations, we can use 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*][B]c = 7[/B]
[*][B]s = 4[/B]
[/LIST]

The revenue for selling x candles is given by f(x)=12x. The teams profit is $40 less than 80% of the

The revenue for selling x candles is given by f(x)=12x. The teams profit is $40 less than 80% of the revenue of selling x candles. write a function g to model the profit.
Profit = Revenue - Cost
We are given the revenue function f(x) = 12x. We are told the profit is 0.8(Revenue) - 40. Our profit function P(x) is:
P(x) = 0.8(12x) - 40
Simplifying, we have:
[B]P(x) = 9.6x - 40[/B]

The school is selling potted plants as a fundraiser. Kara sold 12 ferns and 8 ivy plants for 260.00.

The school is selling potted plants as a fundraiser. Kara sold 12 ferns and 8 ivy plants for 260.00. Paul sold 15 ivy plants and 6 ferns for 240. What’s the selling price of each plant.
Let the cost of each fern be f
Let the cost of each ivy plant be I
We're given:
[LIST=1]
[*]12f + 8i = 260
[*]15i + 6f = 240
[/LIST]
To solve this system of equations, we can use 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12f+%2B+8i+%3D+260&term2=15f+%2B+6i+%3D+240&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12f+%2B+8i+%3D+260&term2=15f+%2B+6i+%3D+240&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12f+%2B+8i+%3D+260&term2=15f+%2B+6i+%3D+240&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]f = 7.5[/B]
[*][B]i= 21.25[/B]
[/LIST]

The senior class at high school A and high school B planned separate trips to the state fair. There

The senior class at high school A and high school B planned separate trips to the state fair. There senior class and high school A rented and filled 10 vans and 6 buses with 276 students. High school B rented and filled 5 vans and 2 buses with 117 students. Every van had the same number of students in them as did the buses. How many students can a van carry?? How many students can a bus carry??
Let b be the number of students a bus can carry. Let v be the number of students a van can carry. We're given:
[LIST=1]
[*]High School A: 10v + 6b = 276
[*]High School B: 5v + 2b = 117
[/LIST]
We have a system of equations. We can solve this 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[LIST]
[*][B]b = 21[/B]
[*][B]v = 15[/B]
[/LIST]

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 5. 5 times the larger number plus 4 times the smaller number is 37. Find the

the sum of 2 numbers is 5. 5 times the larger number plus 4 times the smaller number is 37. Find the numbers
Let the first small number be x. Let the second larger number be y. We're given:
[LIST=1]
[*]x + y = 5
[*]5y + 4x = 37
[/LIST]
We can solve this 3 ways, using the following methods:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[B]x = -12
y = 17
[/B]
Let's check our work using equation 1:
-12 + 17 ? 5
5 = 5 <-- Check
Let's check our work using equation 2:
5(17) + 4(-12) ? 37
85 - 48 ? 37
37 = 37 <-- Check

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 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 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 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 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 for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your

The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your variable and write an equation that models the cost of each bracelet.
We set up a cost function as fixed cost plus total cost. Fixed cost is the shipping charge of $9. So we have the following cost function where n is the cost of the bracelets:
C(b) = nb + 9
We are given C(9) = 72 and b = 9
9n + 9 = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=9n%2B9%3D72&pl=Solve']Run this through our equation calculator[/URL], and we get [B]n = 7[/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 1000 juniors in a college. Among the 1000 juniors, 200 students are taking STAT200, and 10

There are 1000 juniors in a college. Among the 1000 juniors, 200 students are taking STAT200, and 100 students are taking PSYC300. There are 50 students taking both courses.
a) What is the probability that a randomly selected junior is taking at least one of these two courses?
b) What is the probability that a randomly selected junior is taking PSYC300, given that he/she is taking STAT200?
a) P(A U B) = P(A) + P(B) - P(A ? B) = 0.2 + 0.1 - 0.05 = [B]0.25[/B]
b) P(SYC|STAT) = P(STAT ? SYC)/P(STAT) = 0.05/0.2 = [B]0.25[/B]

There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. How

There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. How many of each animal are there?
Chickens have 2 legs, pigs have 4 legs. Let c be the number of chickens and p be the number of pigs. Set up our givens:
(1) c + p = 13
(2) 2c + 4p = 40
[U]Rearrange (1) to solve for c by subtracting p from both sides:[/U]
(3) c = 13 - p
[U]Substitute (3) into (2)[/U]
2(13 - p) + 4p = 40
26 - 2p + 4p = 40
[U]Combine p terms[/U]
2p + 26 = 40
[U]Subtract 26 from each side:[/U]
2p = 14
[U]Divide each side by 2[/U]
[B]p = 7[/B]
[U]Substitute p = 7 into (3)[/U]
c = 13 - 7
[B]c = 6[/B]
For a shortcut, you could use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+p+%3D+13&term2=2c+%2B+4p+%3D+40&pl=Cramers+Method']simultaneous equations calculator[/URL]

There are 2 consecutive integers. Twice the first increased by the second yields 16. What are the nu

There are 2 consecutive integers. Twice the first increased by the second yields 16. What are the numbers?
Let x be the first integer. y = x + 1 is the next integer. We have the following givens:
[LIST=1]
[*]2x + y = 16
[*]y = x + 1
[/LIST]
Substitute (2) into (1)
2x + (x + 1) = 16
Combine x terms
3x + 1 = 16
Subtract 1 from each side
3x = 15
Divide each side by 3
[B]x = 5[/B]
So the other integer is 5 + 1 = [B]6[/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 is a stack of 10 cards, each given a different number from 1 to 10. suppose we select a card r

There is a stack of 10 cards, each given a different number from 1 to 10. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an odd number and the second card is greater than 7.
First Event: P(1, 3, 5, 7, 9) = 5/10 = 1/2 or 0.5
Second Event: P(8, 9, 10) = 3/10 or 0.3
Probability of both events since each is independent is 1/2 * 3/10 = 3/20 = [B]0.15 or 15%[/B]

There were 175 tickets sold for the upcoming event in the gym. If students tickets cost $5 and adult

There were 175 tickets sold for the upcoming event in the gym. If students tickets cost $5 and adult tickets are $8, tell me how many tickets were sold if gate receipts totaled $1028?
Let s be the number of student tickets and a be the number of adult tickets. We are given:
a + s = 175
8a + 5s = 1028
There are 3 ways to solve this, all of which give us:
[B]a = 51
s = 124
[/B]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Substitution']Substitution Method[/URL]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Elimination']Elimination Method[/URL]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Cramers+Method']Cramers Method[/URL]

Thin Lens Distance

Given two out of three items in the thin lens equation, this solves for the third.

Three people went to lunch and bought a large meal which they all split. The total cost, including t

Three people went to lunch and bought a large meal which they all split. The total cost, including tip, was $30. Each person paid $10 to the waitress and started to leave the restaurant. As they left, the waitress came running up to them with five dollars saying that she made a mistake and that the meal and tip should have cost only $25.
The waitress then gave each person one dollar, but didn't know how to split the remaining two dollars. They told her to keep the extra two dollars as an additional tip.
When the people started talking about what had just happened, they started getting confused. They had each paid $10 for the meal and received one dollar back, so they each really paid $9 for the meal for a total of $27. Add the two dollars of extra tip and the total is $29. Where did the extra one dollar go?
[B]The missing dollar is not really missing. The cost of the meal is really $27. The $25 plus the extra two dollar tip was given to the waitress -- $27
What we have is the cost ($27) plus the refund ($3) = $30.
The $30 that was originally paid is accounted for as follows:
Restaurant + regular waitress tip: $25
Three people: $3 (refund)
Waitress: $2 (extra tip)
$25 + $3 + $2 = $30[/B]

Tina's mom made brownies. When tinas friend came over they ate 1/3 of the brownies. Her sister ate 2

Tina's mom made brownies. When tinas friend came over they ate 1/3 of the brownies. Her sister ate 2 and her dad ate 4. If there are 26 brownies left. How many did her mom make
Let b denote the number of brownies Tina's mom made. We're given:
b - 1/3b - 2 - 4 = 26
Combining like terms, we have:
2b/3 - 6 = 26
Add 6 to each side, we get:
2b/3 = 32
To solve this equation for b, we [URL='https://www.mathcelebrity.com/prop.php?num1=2b&num2=32&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
b = [B]48[/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 convert from Celsius to Fahrenheit, multiply by 1.8 and add 32. Write a formula to describe this

To convert from Celsius to Fahrenheit, multiply by 1.8 and add 32. Write a formula to describe this relationship.
Given C as Celsius and F as Fahrenheit, we have the following equation:
[B]F = 1.8C + 32[/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 rent a car it costs $12 per day and $0.50 per kilometer traveled. If a car were rented for 5 days

To rent a car it costs $12 per day and $0.50 per kilometer traveled. If a car were rented for 5 days and the charge was $110.00, how many kilometers was the car driven?
Using days as d and kilometers as k, we have our cost equation:
Rental Charge = $12d + 0.5k
We're given Rental Charge = 110 and d = 5, so we plug this in:
110 = 12(5) + 0.5k
110 = 60 + 0.5k
[URL='https://www.mathcelebrity.com/1unk.php?num=60%2B0.5k%3D110&pl=Solve']Plugging this into our equation calculator[/URL], we get:
[B]k = 100[/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]

Torus

Calculates the volume of a torus and surface area of a torus given major radius and minor radius.

Total Revenue

Given a quantity, price, and item, this calculates the total revenue.

Trapezoids

This calculator determines the following items for a trapezoid based on given inputs:

* Area of trapezoid

* Perimeter of a Trapezoid

* Area of trapezoid

* Perimeter of a Trapezoid

triangle sum theorem

The triangle sum theorem states the sum of the three angles in a triangle equals 180 degrees.
So if you're given two angles and need too find the 3rd angle, add the 2 known angles up, and subtract them from 180 to get the 3rd angle measure.

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

Trigonometry Relations

Calculates various trigonometry measurements (sin,cos,tan,csc,sec,cot) given other measurements that you enter.

Trimmed Mean and Winsorized Mean

Given a number set and a trimmed mean percentage, this will calculate the trimmed mean (truncated mean) or winsorized mean.

Twice a first number decreased by a second number is 16. The first number increased by 3 times the s

Twice a first number decreased by a second number is 16. The first number increased by 3 times the second number is 1. Find the numbers.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]2x - y = 16
[*]x + 3y = 1
[/LIST]
Using our simultaneous equations calculator, you can solve this 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+y+%3D+16&term2=x+%2B+3y+%3D+1&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+y+%3D+16&term2=x+%2B+3y+%3D+1&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+y+%3D+16&term2=x+%2B+3y+%3D+1&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter what method we use, we get the same answers:
[B]x = 7
y = -2
(x, y) = (7, -2)
[/B]
Let's check our work in equation 1:
2(7) - -2 ? 16
14 + 2 ? 16
16 = 16 <-- Check
Let's check our work in equation 2:
7 + 3(-2) ? 1
7 - 6 ? 1
1 = 1 <-- Check

two numbers have an average of 2100 and one number is $425 more than the other number. What are the

two numbers have an average of 2100 and one number is $425 more than the other number. What are the numbers
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*](x + y)/2 = 2100 (Average)
[*]y = x + 425
[/LIST]
Rearrange equation (1) by cross multiplying
x + y = 2 * 2100
x + y = 4200
So we have our revised set of equations:
[LIST=1]
[*]x + y = 4200
[*]y = x + 425
[/LIST]
Substituting equation (2) into equation (1) for y, we get:
x + (x + 425) = 4200
Combining like terms, we get:
2x + 425 = 4200
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B425%3D4200&pl=Solve']equation solver[/URL], we get:
x = [B]1887.5[/B]
Which means using equation (2), we get
y = 1887.5 + 425
y = [B]2312.5[/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 numbers total 83 and have a difference of 17 find the two numbers

Let the numbers be x and y. Set up our givens:
[LIST=1]
[*]x + y = 83
[*]x - y = 17
[*]Rearrange (2), by adding y to each side, we have: x = 17 + y
[/LIST]
[U]Substitute (3) into (1):[/U]
(17 + y) + y = 83
[U]Group y terms[/U]
2y + 17 = 83
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2y%2B17%3D83&pl=Solve']equation solver[/URL], we get:[/U]
[B]y = 33
[/B]
[U]Substitute that into (3)[/U]
x = 17 + 33
[B]x = 50
[/B]
So our two numbers (x, y) = (33, 50)

Tyrone re sells 3 pairs of Yeezys and a pair of Nikes for 250$. Nucci re sells a pair of Yeezys and

Tyrone re sells 3 pairs of Yeezys and a pair of Nikes for 250$. Nucci re sells a pair of Yeezys and Nikes for 150$ How much does a pair of Yeezys cost?
Let y be the cost of Yeezy's and n be the cost of Nike's. We're given two equations:
[LIST=1]
[*]3y + n = 250
[*]y + n = 150
[/LIST]
We have a system of equations, and we can solve it using one of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3y+%2B+n+%3D+250&term2=y+%2B+n+%3D+150&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3y+%2B+n+%3D+250&term2=y+%2B+n+%3D+150&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3y+%2B+n+%3D+250&term2=y+%2B+n+%3D+150&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]n = 100[/B]
[*][B]y = 50[/B]
[/LIST]

Units of Output (Service Output) Depreciation

Given an asset value, salvage value, production units, and units per period, this calculates the depreciation per period using the units of output depreciation (service output depreciation)

Utility and Cost Utility Ratio

Given 2 methods with a set of utilities and weights/probabilities, this will calculate the utility for each method, as well as the total utility using the additive method, as well as the Cost Utility Ratio

Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that s

Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that starts with 13 and continues to add seven to each output. For now, van needs to know what the 15th output will be. Complete the steps needed to determine the 15th term in sequence.
Given a first term a1 of 13 and a change amount of 7, expand the series
The explicit formula for an [I]arithmetic series[/I] is an = a1 + (n - 1)d
d represents the common difference between each term, an - an - 1
Looking at all the terms, we see the common difference is 7, and we have a1 = 13
Therefore, our explicit formula is an = 13 + 7(n - 1)
If n = 15, then we plug it into our explicit formula above:
an = 13 + 7(n - 1)
a(15) = 15 + 7(15 - 1)
a(15) = 15 + 7 * 14
a(15) = 15 + 98
a(15) = [B]113[/B]

Vectors

Given 2 vectors A and B, this calculates:

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj_{B}A and and the vector component of A orthogonal to B → A - proj_{B}A

Also calculates the horizontal component and vertical component of a 2-D vector.

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj

Also calculates the horizontal component and vertical component of a 2-D vector.

Venn Diagram (2 circles)

Given two circles A and B with an intersection piece of C, this will calculate all relevant probabilities of the Venn Diagram.

Verbal Phrase

Given an algebraic expression, this translates back to a verbal phrase

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]

Volatility

Given a set of stock prices, this determines expected rates of return and volatility

Walking Distance (Pedometer)

Given a number of steps and a distance per stride in feet, this calculator will determine how far you walk in other linear measurements.

Warren was making $100,000 per year. His boss said that he was going to cut his salary 25%, but that

Warren was making $100,000 per year. His boss said that he was going to cut his salary 25%, but that Warren shouldn't worry because he would be given a 25% raise the next day. How much will Warren's salary be after the 25% cut and 25% raise?
Cut salary:
100,000 * 0.75 = 75,000
New salary after raise:
75,000 * 1.25 = [B]93,750[/B]

Weighted Average Cost of Capital (WACC) and Capital Asset Pricing Model (CAPM)

Calculates the Weighted Average Cost of Capital (WACC) and also calculates the return on equity if not given using the Capital Asset Pricing Model (CAPM) using debt and other inputs such as Beta and risk free rate.

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 formula for the area of a circle?

What is the formula for the area of a circle?
Given a radius r, we have Area (A) of:
[B]A = ?r^2[/B]

What is the formula for the circumference of a circle?

What is the formula for the circumference of a circle?
Given radius r and diameter d, the circumference C is:
[B]C = 2?r or ?d[/B]

Which of the following equations represents a line that is parallel to the line with equation y = -3

Which of the following equations represents a line that is parallel to the line with equation y = -3x + 4?
A) 6x + 2y = 15
B) 3x - y = 7
C) 2x - 3y = 6
D) x + 3y = 1
Parallel lines have the same slope, so we're looking for a line with a slope of 3, in the form y = mx + b. For this case, we want a line with a slope of -3, like our given line.
If we rearrange A) by subtracting 6x from each side, we get:
2y = -6x + 15
Divide each side by 2, we get:
y = -3x + 15/2
This line is in the form y = mx + b, where m = -3. So our answer is [B]A[/B].

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

Wind Chill Factor

This calculator determines the wind chill factor given a temperature in F° and a wind speed in miles per hour (mph). Simply enter your temperature and wind speed and press the button

Work Word Problems

Given Person or Object A doing a job in (r) units of time and Person or Object B doing a job in (s) units of time, this calculates how long it would take if they combined to do the job.

Write an equation in slope-intercept form for the line with slope 4 and y-intercept -7

Write an equation in slope-intercept form for the line with slope 4 and y-intercept -7
The standard equation for slope (m) and y-intercept (b) is given as:
y = mx + b
We're given m = 4 and y-intercept = -7, so we have:
[B]y = 4x - 7[/B]

Yolanda is riding her bicycle. She rides for 5 hours at a speed of 12.5 kilometers per hours. For ho

Yolanda is riding her bicycle. She rides for 5 hours at a speed of 12.5 kilometers per hours. For how many kilometers does she ride?
This is a distance problem, where distance = rate * time. We are given time of 5 hours, at a rate of 12.5km/hour.
Using our [URL='http://www.mathcelebrity.com/drt.php?d=+&r=12.5&t=5&pl=Calculate+the+missing+Item+from+D%3DRT']distance calculator[/URL], we get D = [B]62.5km[/B].

Yosemite National Park charges $7 per person for an all day admission to the park. The total cost fo

Yosemite National Park charges $7 per person for an all day admission to the park. The total cost for n people to go to the park all day is given by the expression 7n. 8 friends go to the park on Saturday. What is the total cost of admission?
We want to evaluate f(n) = 7n for n = 8
f(8) = 7(8) = [B]56[/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 given a choice of taking the simple interest on $100,000 invested for 5 years at a rate of 2

You are given a choice of taking the simple interest on $100,000 invested for 5 years at a rate of 2% or the interest on $100,000 invested for 5 years at an interest rate of 2% compounded daily. Which investment earns the greater amount of interest? Give the difference between the amounts of interest earned by the two investments
[URL='http://www.mathcelebrity.com/simpint.php?av=&p=100000&int=2&t=5&pl=Simple+Interest']Simple interest balance after 5 years[/URL] at 2% is $110,000.
[URL='http://www.mathcelebrity.com/compoundint.php?bal=100000&nval=1825&int=2&pl=Daily']Daily compounded interest for 5 years[/URL] at 2% is 365 days per year * 5 years = 1,825 days = [B]$110,516.79
Compound interest earns more by $110,516.79 - $110,000 = $516.79[/B]

You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet.

You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet. Company A charges $2.99 per square foot plus a $200 installation charge. Company B charges $19.99 per square yard plus a $500 installation charge. What is the best deal?
Did you notice the word snuck in on this problem? Company B is given in square [I][B]yards[/B][/I], not feet. Let's convert their price to square feet to match company A.
[U]Company B conversion:[/U]
Since we have 1 square yard = 3 feet * 3 feet = 9 square feet, we need to solve the following proportion:
$19.99/square yard * 1 square yard/9 feet = $19.99 square yard / 9 feet = $2.22 / square foot.
Now, let's set up the cost equations C(s) for each Company in square feet (s)
[LIST]
[*]Company A: C(s) = 200 + 2.99s
[*]Company B: C(s) = 500 + 2.22s
[/LIST]
The problem asks for s = 30 feet * 50 feet = 1500 square feet. So we want to calculate C(1500)
[U]Company A:[/U]
C(1500) = 200 + 2.99(1500)
C(1500) = 200 + 4485
C(1500) = 4685
[U]Company B:[/U]
C(1500) = 500 + 2.22(1500)
C(1500) = 500 + 3330
C(1500) = 3830
Since [B]Company B[/B] has the lower cost per square foot, they are the better buy.

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 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 choose an alpha level of .01 and then analyze your data.

(a) What is the probability that

You choose an alpha level of .01 and then analyze your data.
(a) What is the probability that you will make a Type I error given that the null hypothesis is true?
(b) What is the probability that you will make a Type I error given that the null hypothesis is false.
[B](a) 0.01. Instead, α is the probability of a Type I error given that the null hypothesis is true. If the null hypothesis is false, then it is impossible to make a Type I error.[/B]
[B](b) Impossible Instead, α is the probability of a Type I error given that the null hypothesis is true. If the null hypothesis is false, then it is impossible to make a Type I error.[/B]

You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must yo

You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must you leave the money in the account to earn $500 in interest?
The simple interest formula for the accumulated balance is:
I = Prt
We are given P = 2,000, r = 0.04, and I = 500.
500 = 2000(0.04)t
80t = 500
Divide each side by 80
t = 6.25 years.

You deposit $750 in an account that earns 5% interest compounded quarterly. Show and solve a functio

You deposit $750 in an account that earns 5% interest compounded quarterly. Show and solve a function that represents the balance after 4 years.
The Accumulated Value (A) of a Balance B, with an interest rate per compounding period (i) for n periods is:
A = B(1 + i)^n
[U]Givens[/U]
[LIST]
[*]4 years of quarters = 4 * 4 = 16 quarters. So this is t.
[*]Interest per quarter = 5/4 = 1.25%
[*]Initial Balance (B) = 750.
[/LIST]
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=750&nval=16&int=5&pl=Quarterly']compound balance interest calculator[/URL], we get the accumulated value A:
[B]$914.92[/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 $80. Jeans cost $29 and shirts cost $12. Mom told you to buy one pair of jeans and use the

You have $80. Jeans cost $29 and shirts cost $12. Mom told you to buy one pair of jeans and use the rest of the money to buy shirts. Find the inequality.
Let j be the number of jeans. Let s be the number of shirts. We are given:
[LIST]
[*]Mom told you to buy one pair of jeans. So we have $80 to start with - $29 for 1 pair of jeans = $51 left over
[/LIST]
Now, since shirts cost $12 each, and our total number of shirts we can buy is s, our inequality is [B]12s <= 51[/B].
We want to find the s that makes this inequality true.
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=12s%3C%3D51&pl=Show+Interval+Notation']Run this statement through our calculator[/URL], and we get s <= 4.25. But, we need s to be an integer, so we have s <= 4.

You roll a red die and a green die. What is the size of the sample space of all possible outcomes of

You roll a red die and a green die. What is the size of the sample space of all possible outcomes of rolling these two dice, given that the red die shows an even number and the green die shows an odd number greater than 1?
[LIST]
[*]Red Die Sample Space {2, 4, 6}
[*]Green Die Sample Space {3, 5}
[*]Total Sample Space {(2, 3), (2, 5), (4, 3), (4, 5), (6, 3), (6, 5)}
[*]The sie of this is 6 elements.
[/LIST]

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 grade must be at least 60 to pass this class

Your grade must be at least 60 to pass this class
Assumptions and givens:
[LIST]
[*]The phrase [I]at least[/I] means greater than or equal to.
[*]Let g be your grade
[/LIST]
We have:
[B]g >= 60[/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 profit for mowing lawns this week is $24. You are paid $8 per hour and you paid $40 for gas for

Your profit for mowing lawns this week is $24. You are paid $8 per hour and you paid $40 for gas for the lawn mower. How many hours did you work this week?
We know profit from the equation below:
Revenue - Cost = Profit
We're given Profit as 42, so we have:
Revenue - Cost = 42
Let hours worked be h. We have revenue as:
Revenue = 8h
Cost = 40, so we plug these into profit to get:
8h - 40 = 42
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h-40%3D42&pl=Solve']plug this equation into our math engine[/URL] and get:
h = [B]10.25[/B]

Z Score Lookup

Given a Z-score probability statement from the list below, this will determine the probability using the normal distribution z-table.

* P(z < a)

* P(z <= a)

* P(z > a)

* P(z >= a)

* P(a < z < b) Calculates z score probability

* P(z < a)

* P(z <= a)

* P(z > a)

* P(z >= a)

* P(a < z < b) Calculates z score probability

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]

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]

Zero-Coupon Bond Price

This calculator calculates the price of a zero-coupon bond given a face value, yield rate, and term.