times - Another word for multiply

$300 for 13 years at 8% compounded semiannually. P=principle = original funds, r=rate, in percent, w

$300 for 13 years at 8% compounded semiannually. P=principle = original funds, r=rate, in percent, written as a decimal (1%=.01, 2%=.02,etc) , n=number of times per year, t= number of years
So we have:
[LIST]
[*]$300 principal
[*]13 * 2 = 26 periods for n
[*]Rate r for a semiannual compound is 8%/2 = 4% per 6 month period
[/LIST]
Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=300&int=4&t=26&pl=Compound+Interest']compound interest with balance calculator[/URL], we get:
[B]$831.74[/B]

(n^2)^3 without exponents

(n^2)^3 without exponents
This expression evaluates to:
n^(2 *3)
n^6
To write this without exponents, we expand n times itself 6 times:
[B]n * n * n * n * n * n[/B]

-10 times the quantity y minus 4

-10 times the quantity y minus 4
The quantity y minus 4:
y - 4
10 times this quantity:
[B]10(y - 4) [/B]

-2 times the quantity q minus 3

-2 times the quantity q minus 3
q minus 3:
q - 3
-2 times the quantity:
-2(q - 3)

-2 times the quantity t plus 7

-2 times the quantity t plus 7
The key word here is quantity. In this case, the quantity is t plus 7
t + 7
-2 times the quantity means we multiply -2 times the quantity t + 7
[B]-2(t + 7)
[MEDIA=youtube]nUWLUPfX52k[/MEDIA][/B]

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

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

1 integer is 7 times another. If the product of the 2 integers is 448, then find the integers.

1 integer is 7 times another. If the product of the 2 integers is 448, then find the integers.
Let the first integer be x and the second integer be y. We have the following two equations:
[LIST=1]
[*]x = 7y
[*]xy = 448
[/LIST]
Substitute (1) into (2), we have:
(7y)y = 448
7y^2 = 448
Divide each side by 7
y^2 = 64
y = -8, 8
We use 8, since 8*7 = 56, and 56*8 =448. So the answer is [B](x, y) = (8, 56)[/B]

1 rabbit saw 9 elephants while going to the river. Every elephant saw 3 monkeys going to the river.

1 rabbit saw 9 elephants while going to the river. Every elephant saw 3 monkeys going to the river. Each monkey had 1 tortoise in each hand. How many animals are going to the river?
Trick question:
The elephants [U]are not[/U] going to the river.
So 1 rabbit goes to the river
3 monkeys go to the river, each holding a tortoise in [B]each hand[/B]. 2 hands per money times 3 monkeys = 6 tortoises
So we have 1 rabbit + 3 monkeys + 6 tortoises = [B]10 animals[/B]

1/3 a number increased by 10 times by that same number

1/3 a number increased by 10 times by that same number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
1/3 a number
1/3 * x = x/3
That same number means the same arbitrary variable as above:
x
10 times that same number:
10x
The phrase [I]increased by[/I] means we add:
[B]x/3 + 10x
[MEDIA=youtube]29TGt3i28jw[/MEDIA][/B]

1/3 times q plus 5 equal q minus 4

1/3 times q plus 5 equal q minus 4
1/3 times q plus 5:
(q + 5)/3
q minus 4:
q - 4
The word [I]equal[/I] means we set (q + 5)/3 equal to q - 4:
[B](q + 5)/3 = q - 4[/B]

1/6 times the sum k and 5

1/6 times the sum k and 5
The sum k and 5
(k + 5)
1/6 times the sum k and 5
(k + 5)/6

10 times a number is 420

10 times a number is 420
A number denotes an arbitrary variable, let's call it x.
10 times a number:
10x
The phrase is means equal to, so we set 10x equal to 420
[B]10x = 420 <-- This is our algebraic expression
[/B]
If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=10x%3D420&pl=Solve']equation calculator[/URL]
We get x = 42

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

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

10 times the square of a number w divided by 12

10 times the square of a number w divided by 12
The square of a number w
w^2
10 times this
10w^2
Divided by 12
[B]10w^2/12[/B]

104 subtracted from the quantity 6 times r is the same as r

104 subtracted from the quantity 6 times r is the same as r
The quantity 6 times r means we multiply 6 by r:
6r
104 subtracted from 6r is written as:
6r - 104
[B]The phrase [I]is the same as[/I] means we have an equation. So we set 6r - 104 equal to r
6r - 104 = r[/B]

108 times a, reduced by 147 is k subtracted from 56

108 times a, reduced by 147 is k subtracted from 56
Take this algebraic expression in pieces:
Step 1: 108 times a:
108a
Step 2: Reduced by means subtract, so we subtract 47 from 108a:
108a - 47
Step 3: ksubtracted from 56:
56 - k
Step 4: The phrase [I]is[/I] means equal to, so we set 108a - 47 equal to 56 - k
[B]108a - 47 = 56 - k
[MEDIA=youtube]KrY6uzKeeB0[/MEDIA][/B]

11 combination of 3 times 6 combination of 3

11 combination of 3 times 6 combination of 3
[URL='https://www.mathcelebrity.com/permutation.php?num=11&den=3&pl=Combinations']11 combination of 3[/URL] = 165
[URL='https://www.mathcelebrity.com/permutation.php?num=6&den=3&pl=Combinations']6 combination of 3[/URL] = 20
11 combination of 3 times 6 combination of 3 = 165 * 20
11 combination of 3 times 6 combination of 3 = [B]3300[/B]

12 plus 6 times a number is 9 times the number

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

13 times the sum of x and 9y

13 times the sum of x and 9y
The sum of x and 9y means we add 9y to x:
x + 9y
Now multiply this sum by 13:
[B]13(x + 9y)[/B]

15 added to a number is 16 times the number

15 added to a number is 16 times the number
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]15 added to a number: 15 + x
[*]16 times the number: 16x
[*]The phrase [I]is[/I] means equal to. So we set 15 + x equal to 16x
[/LIST]
[B]15 + x = 16x[/B]

16 decreased by 3 times the sum of 3 and a number

16 decreased by 3 times the sum of 3 and a number
Take this algebraic expression in parts:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[*]The sum of 3 and a number: 3 + x
[*]3 times the sum: 3(3 + x)
[*]16 decreased by... means we subtract 3(3 + x) from 16
[/LIST]
[B]3(3 + x) from 16[/B]

17 decreased by three times d equals c

17 decreased by three times d equals c
three times d means we multiply d by 3:
3d
17 decreased by three times d means we subtract 3d from 17
17 - 3d
The word [I]equals[/I] means an equation, so we set 17 - 3d equal to c:
[B]17 - 3d = c[/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 less than 3 times n is 4 more than n

2 less than 3 times n is 4 more than n
3 times n:
3n
2 less than 3 times n
3n - 2
4 more than n:
n + 4
The word [I]is[/I] means equal to, so we set 3n - 2 equal to n + 4:
[B]3n - 2 = n + 4[/B]

2 minus 7 times a number

A number is represented by an arbitrary variable, let's call it x.
7 times x means we multiply 7 times x.
7x
2 minus 7x is written:
2 - 7x

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

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

2 times a number equals that number plus 5

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

2 times 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 a number subtracted by x

2 times a number subtracted by x
The phrase [I]a number[/I] means an arbitrary variable, let's call it n.
n
2 times a number means we multiply n by 2:
2n
The phrase [I]subtracted by[/I] means we subtract 2n from x:
[B]x - 2n[/B]

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

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

2 times b squared minus 6

2 times b squared minus 6
b squared means we raise b to the 2nd power:
b^2
2 times b squared
2b^2
Minus 6:
[B]2b^2 - 6[/B]

2 times half of a number

A number means an arbitrary variable, let's call it x.
Half of x means we divide x by 2, or multiply by 0.5
x/2
2 times half x is written:
[B]2(x/2)[/B]
If we simplify by cancelling the 2's, we just get x.

2 times itself

2 times itself
Itself means we multiply 2 by 2:
2 * 2
[B]4[/B]

2 times the quantity x minus 1 is 12

2 times the quantity x minus 1 is 12
The quantity x minus 1 is written as:
x - 1
2 times this quantity:
2(x - 1)
The word [I]is[/I] means an equation, so we set 2(x - 1) equal to 12:
[B]2(x - 1) = 12[/B]

2 times the sum of 1 and some number is 30. What is the number?

2 times the sum of 1 and some number is 30. What is the number?
We let the phrase "some number" equal the variable x.
The sum of 1 and some number is:
x + 1
2 times the sum:
2(x + 1)
The word "is" means equal to, so we set [B]2(x + 1) = 30[/B]

2 times the sum of 3 and 5 divided by 10

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

2 times the sum of 3x and 5

2 times the sum of 3x and 5
the sum of 3x and 5
3x + 5
2 times the sum:
[B]2(3x + 5)[/B]

2 times the sum of 7 times a number and 4

2 times the sum of 7 times a number and 4
This is an algebraic expression. Let's take it in 4 parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]7 times a number means we multiply x by 7: 7x
[*]The sum of 7 times a number and 4 means we add 4 to 7x: 7x + 4
[*]Finally, we multiply the sum in #3 by 2
[/LIST]
Build our final algebraic expression:
[B]2(7x + 4)[/B]

2 times the sum of a number and 3 is equal to 3x plus 4

2 times the sum of a number and 3 is equal to 3x plus 4
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 3 means we add 3 to x:
x + 3
2 times this sum means we multiply the quantity x + 3 by 2
2(x + 3)
3x plus 4 means 3x + 4 since the word plus means we use a (+) sign
3x + 4
The phrase [I]is equal to[/I] means an equation, where we set 2(x + 3) equal to 3x + 4
[B]2(x + 3) = 3x + 4[/B]

2 times the sum of a number x and 5

2 times the sum of a number x and 5
The sum of a number x and 5 means we add 5 to x:
x + 5
2 times the sum:
[B]2(x + 5)[/B]

2 times the sum of x and 7 plus 10

2 times the sum of x and 7 plus 10
The sum of x and 7 means we add 7 to x
x + 7
2 times the sum means we multiply the quantity x + 7 by 2
2(x + 7)
Plus 10 means we add 10 to the 2(x + 7):
[B]2(x + 7) + 10[/B]

2 times x divided by 4 times y

2 times x divided by 4 times y
2 times x:
2x
4 times y:
4y
2 times x divided by 4 times y
[B]2x/4y[/B]

2 times x squared minus 4 times x

2 times x squared minus 4 times x
2x^2 - 4x

2 traffic lights are turned on at the same time. 1 blinks every 4 seconds and. the other blinks ever

2 traffic lights are turned on at the same time. 1 blinks every 4 seconds and. the other blinks every 6 seconds. In 60 seconds how many times will they blink at the same time?
We want the [URL='https://www.mathcelebrity.com/gcflcm.php?num1=4&num2=6&num3=&pl=LCM']least common multiple of 4 and 6[/URL] which is 12.
So ever 12 seconds, both lights blink together:
[LIST=1]
[*]12
[*]24
[*]36
[*]48
[*]60
[/LIST]
So our answer is [B]5 times[/B]

217 times u, reduced by 180 is the same as q

217 times u, reduced by 180 is the same as q.
Take this algebraic expression pieces:
Step 1: 217 times u
We multiply the variable u by 217
217u
Step 2: reduced by 180
Subtract 180 from 217u
217u - 180
The phrase [I]is the same as[/I] means an equation, so we set 217u - 180 equal to q
[B]217u - 180 = q[/B]

223 subtracted from the quantity 350 times a is equal to b

223 subtracted from the quantity 350 times a is equal to b
Take this algebraic expression in parts:
[LIST]
[*]the quantity 350 times a: 350a
[*]223 subtracted from the quantity: 350a - 223
[*]The phrase [I]is equal to[/I] means an equation, so we set 350a - 223 equal to b
[/LIST]
[B]350a - 223 = b[/B]

231 is 248 subtracted from the quantity h times 128

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

249 equals 191 times c, decreased by 199

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

26 increased by 12 times a number

26 increased by 12 times a number
A number is represented by an arbitrary variable, let's call it x
12 times a number is written as 12x
26 increased by 12 times a number means we add:
[B]26 + 12x[/B]

2consecutiveevenintegerssuchthatthesmalleraddedto5timesthelargergivesasumof70

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

2x increased by 3 times a number

2x increased by 3 times a number
The phrase [I]a number[/I] means an arbitary variable, let's call it x.
3 times a number means we multiply x by 3:
3x
The phrase [I]increased by[/I] means we add 3x to 2x:
2x + 3x
Simplifying, we get:
[B]5x[/B]

2^46 is how many times as many as 2^42

2^46 is how many times as many as 2^42
We can break this apart as follows:
2^46 = 2^42 * [B]2^4[/B]

3 decreased by 7 times a number

3 decreased by 7 times a number
A number signifies an arbitrary variable, let's call it x.
7 times a number:
7x
3 decreased by this means we subtract 7x
[B]3 - 7x[/B]

3 less than a number times itself

3 less than a number times itself
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Itself means the same variable as above. So we have:
x * x
x^2
3 less than this means we subtract 3 from x^2:
[B]x^2 - 3[/B]

3 times a number increased by 1 is between -8 and 13

3 times a number increased by 1 is between -8 and 13.
Let's take this algebraic expression in [U]4 parts[/U]:
Part 1 - The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Part 2 - 3 times this number means we multiply x by 3:
3x
Part 3 - Increased by 1 means we add 1 to 3x:
3x + 1
The phrase [I]between[/I] means we have an inequality:
[B]-8 <= 3x + 1 <=13[/B]

3 times a number is 3 more a number

3 times a number is 3 more a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
3 times a number:
3x
3 more than a number means we add 3 to x:
x + 3
The word [I]is[/I] means and equation, so we set 3x equal to x + 3
[B]3x = x + 3[/B]

3 times larger than the sum of 4 and 9

The sum of 4 and 9:
4 + 9
3 times larger than this sum
[B]3(4 + 9) <-- This is our algebraic expression
[/B]
Evaluating this amount:
3(13)
[B]39[/B]

3 times the difference between t and y

3 times the difference between t and y
Difference between t and y
t - y
3 times this difference:
[B]3(t - y)[/B]

3 times the difference of a and b is equal to 4 times c

3 times the difference of a and b is equal to 4 times c
[U]The difference of a and b:[/U]
a - b
[U]3 times the difference of a and b:[/U]
3(a - b)
[U]4 times c:[/U]
4c
The phrase [I]is equal to[/I] means an equation. So we set 3(a - b) equal to 4c:
[B]3(a - b) = 4c[/B]

3 times the difference of x and 5 is 15

The difference of x and 5 means we subtract:
x - 5
3 times the difference means we multiply (x - 5) by 3
3(x - 5)
Is, means equal to, so we set our expression equal to 15
[B]3(x - 5) = 15
[/B]
If you need to take it one step further to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3%28x-5%29%3D15&pl=Solve']equation calculator[/URL]

3 times the quantity 2 decreased by x is 9

3 times the quantity 2 decreased by x is 9
The quantity 2 decreased by x. The phrase [I]decreased by[/I] means we subtract:
2 - x
3 times the quantity:
3(2 - x)
The word [I]is[/I] means equal to, so we set 3(2 - x) equal to 9:
[B]3(2 - x) = 9
[MEDIA=youtube]Hzyt_GajZA4[/MEDIA][/B]

3 times the square of a number x minus 12

3 times the square of a number x minus 12.
Build the algebraic expression piece by piece:
[LIST]
[*]Square of a number x: x^2
[*]3 times this: 3x^2
[*]Minus 12: [B]3x^2 - 12[/B]
[/LIST]

3 times the sum of 2 decreased by x is 9

3 times the sum of 2 decreased by x is 9
2 decreased by x:
2 - x
3 times the sum means we multiply 2 - x by 3:
3(2 - x)
The phrase [I]is 9[/I] means equal to, so we set 3(2 - x) equal to 9:
[B]3(2 - x) = 9[/B]

3 times the sum of twice k and 8

3 times the sum of twice k and 8
Twice k means we multiply k by 2:
2k
The sum of twice k and 8:
2k + 8
3 times the sum:
[B]3(2k + 8)[/B]

3 times the sum of x and 9y

3 times the sum of x and 9y
The sum of x and 9y means we add 9y to x:
x + 9y
Now we take this sum, and multiply by 3 to get our final algebraic expression:
3(x + 9y)

3 times the width plus 2 times the length

3 times the width plus 2 times the length
Let w be the width
Let l be the length
We have an algebraic expression of:
[B]3w + 2l[/B]

3 times x minus y is 5 times the sum of y and 2 times x

3 times x minus y is 5 times the sum of y and 2 times x
Take this algebraic expression in pieces:
3 times x:
3x
Minus y means we subtract y from 3x
3x - y
The sum of y and 2 times x mean we add y to 2 times x
y + 2x
5 times the sum of y and 2 times x:
5(y + 2x)
The word [I]is[/I] means an equation, so we set 3x - y equal to 5(y + 2x)
[B]3x - y = 5(y + 2x)[/B]

3 times x squared minus 4 times x

3 times x squared minus 4 times x
[U]x squared[/U]
x^2
[U]3 times x squared:[/U]
3x^2
[U]4 times x:[/U]
4x
[U]3 times x squared minus 4 times x[/U]
[B]3x^2 - 4x[/B]

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

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

30 increased by 3 times the square of a number

Let "a number" equal the arbitrary variable x.
The square of that is x^2.
3 times the square of that is 3x^2.
Now, 30 increased by means we add 3x^2 to 30
30 + 3x^2

30 increased by 3 times the square of a number

30 increased by 3 times the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The square of a number means we raise x to the power of 2:
x^2
3 times the square:
3x^2
The phrase [I]increased by[/I] means we add 3x^2 to 30:
[B]30 + 3x^2[/B]

300 reduced by 5 times my age is 60

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

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

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

324 times z, reduced by 12 is z

324 times z, reduced by 12 is z.
Take this algebraic expression in pieces:
324 [I]times[/I] z means we multiply 324 by the variable z.
324z
[I]Reduced by[/I] 12 means we subtract 12 from 324z
324z - 12
The word [I]is[/I] means we have an equation, so we set 324z - 12 equal to z
[B]324z - 12 = z [/B] <-- This is our algebraic expression

339 equals 303 times w, minus 293

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

346 times w, decreased by 79 equals w

346 times w, decreased by 79 equals w
346 times w
346w
Decreased by 79
346w - 79
Equals w
[B]346w - 79 = w[/B]

365 subtracted from the quantity q times 146 is the same as w

[U]q times 146:[/U]
146q
[U]365 subtracted from that:[/U]
146q - 365
[U]Is the same as means equal to, so we have:[/U]
[B]146q - 365 = w[/B]

3abc^4/12a^3(b^3c^2)^2 * 8ab^-4c/4a^2b

3abc^4/12a^3(b^3c^2)^2 * 8ab^-4c/4a^2b
Expand term 1:
3abc^4/12a^3(b^3c^2)^2
3abc^4/12a^3b^6c^4
Now simplify term 1:
3/12 = 1/4
c^4 terms cancel
Subtract powers from variables since the denominator powers are higher:
b^(6 - 1) = b^5
a^(3 - 1) = a^2
1/4a^2b^5
Now simplify term 2:
8ab^-4c/4a^2b
8/4 = 2
2c/a^(2 - 1)b^(1 - -4)
2c/ab^5
Now multiply simplified term 1 times simplified term 2:
1/4a^2b^5 * 2c/ab^5
(1 * 2c)/(4a^2b^5 * ab^5)
2c/4a^(2 + 1)b^(5 + 5)
2c/4a^3b^10
2/4 = 1/2, so we have:
[B]c/2a^3b^10[/B]

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

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

4 times 8 to the sixth power

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

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

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

4 times a number cubed decreased by 7

4 times a number cubed decreased by 7
A number is denoted as an arbitrary variable, let's call it x
x
Cubed means raise x to the third power
x^3
Decreased by 7 means subtract 7
x^3 - 7

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

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

4 times a number plus 9

A number means an arbitrary variable, let's call it "x".
4 times a number is 4x.
Plus 9 means we add:
4x + 9

4 times b increased by 9 minus twice y

4 times b increased by 9 minus twice y
Take this algebraic expression in parts:
Step 1: 4 times b means we multiply the variable b by 4:
4b
Step 2: Increased by 9 means we add 9 to 4b:
4b + 9
Step 3: Twice y means we multiply the variable y by 2:
2y
Step 4: The phrase [I]minus[/I] means we subtract 2y from 4b + 9
[B]4b + 9 - 2y[/B]

4 times of the sum of the cubes of x and y

4 times of the sum of the cubes of x and y
The cube of x means we raise x to the 3rd power:
x^3
The cube of y means we raise y to the 3rd power:
y^3
The sum of the cubes means we add:
x^3 + y^3
4 times the sum of the cubes:
[B]4(x^3 + y^3)[/B]

4 times the difference of 6 times a number and 7

4 times the difference of 6 times a number and 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
6 times a number
6x
The difference of 6x and 7 means we subtract 7 from 6x:
6x - 7
Now we multiply this difference by 4:
[B]4(6x - 7)[/B]

4 times the number of cows plus 2 times the number of ducks

4 times the number of cows plus 2 times the number of ducks
Let c be the number of cows. Let d be the number of ducks. We've got an algebraic expression below:
[B]4c + 2d[/B]

4 times the quantity of a number plus 6

4 times the quantity of a number plus 6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The word [I]plus[/I] means we addd 6 to x
x + 6
The phrase [I]4 times the quantity [/I]means we multiply x + 6 by 4
[B]4(x + 6)[/B]

4 times the sum of 10 and twice x

4 times the sum of 10 and twice x
Twice x means we multiply x by 2:
2x
The sum of 10 and twice x:
10 + 2x
Now multiply this sum by 4:
[B]4(10 + 2x)[/B]

4 times the sum of 3 plus x squared

4 times the sum of 3 plus x squared
x squared means we raise x to the power of 2:
x^2
3 plus x squared:
3 + x^2
4 times the sum of 3 plus x squared
3(3 + x^2)

4 times the sum of q and p

The sum of q and p is written q + p
4 times the sum of q and p is written as:
[B]4(q + p)[/B]

4 times x plus 2 is at most 10

4 times x plus 2 is at most 10
4 times x
4x
Plus 2
4x + 2
At most means less than or equal to, so we have:
[B]4x + 2 <= 10[/B]

4 times x times y increase by 9

4 times x times y increase by 9
4 times x times y:
4xy
Increase this by 9:
[B]4xy + 9[/B]

4/5 of the sum of k and 3

4/5 of the sum of k and 3
The sum of k and 3 means we add 3 to k:
k + 3
4/5 of the sum means we multiply 4/5 times the sum k + 3:
[B]4(k + 3)/5[/B]

400 reduced by 3 times my age is 214

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

4subtractedfrom6timesanumberis32

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

5 subtracted from 3 times a number is 44

5 subtracted from 3 times a number is 44.
The problem asks for an algebraic expression.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
3 times this number is 3x.
5 subtracted from this is written as 3x - 5.
The phrase [I]is[/I] means an equation, so we set 3x - 5 equal to 44
[B]3x - 5 = 44[/B]

5 times a number increased by 13

5 times a number increased by 13
A number is denoted as an arbitrary variable, let's call it x
x
5 times that number
5x
Increased by 13 means we add
5x + 13

5 times a number increased by 4 is divided by 6 times the same number

5 times a number increased by 4 is divided by 6 times the same number
Take this algebraic expression in parts.
Part 1: 5 times a number increased by 4
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x
[*]5 times the number means multiply x by 5: 5x
[*][I]Increased by 4[/I] means we add 4 to 5x: 5x + 4
[/LIST]
Part 2: 6 times the same number
[LIST]
[*]From above, [I]a number[/I] is x: x
[*]6 times the number means we multiply x by 6: 6x
[/LIST]
The phrase [I]is divided by[/I] means we have a quotient, where 5x + 4 is the numerator, and 6x is the denominator.
[B](5x + 4)/6x[/B]

5 times a number is 4 more than twice a number

5 times a number is 4 more than twice a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
5 times a number:
5x
Twice a number means we multiply x by 2:
2x
4 more than twice a number
2x + 4
The word [I]is[/I] means equal to, so we set 5x equal to 2x + 4
[B]5x = 2x + 4[/B]

5 times a number is that number minus 3

5 times a number is that number minus 3
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[LIST]
[*]5 times a number: 5x
[*]That number means we use the same number from above which is x
[*]That number minus 3: x - 3
[*]The phrase [I]is[/I] means an equation, so we set 5x equal to x - 3
[/LIST]
[B]5x = x - 3[/B]

5 times g reduced by the square of h

5 times g reduced by the square of h
Take this algebraic expression in pieces:
[LIST=1]
[*]5 times g means we multiply g by 5: 5g
[*]The square of h means we raise h to the 2nd power: h^2
[*]5 times g reduced by the square of h means we subtract h^2 from 5g:
[/LIST]
[B]5g - h^2[/B]

5 times quantity n minus 3

5 times quantity n minus 3
quantity n minus 3
(n - 3)
5 times quantity n minus 3
[B]5(n - 3)[/B]

5 times the product of 2 numbers a and b

5 times the product of 2 numbers a and b
The product of 2 numbers a and be means we multiply the variables together:
ab
5 times the product means we multiply ab by 5:
[B]5ab[/B]

5 times the sum of 3 times a number and -5

5 times the sum of 3 times a number and -5
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
3 times a number means we multiply x by 3:
3x
the sum of 3 times a number and -5 means we add -5 to 3x:
3x - 5
5 times the sum means we multiply 3x - 5 by 5:
[B]5(3x - 5)[/B]

5 times the total of 60 and x

5 times the total of 60 and x
The total of 60 and x means we add:
60 + x
5 times the total means we multiply the sum by 5
5(60 + x)

5 times x, divided by 7

5 times x
5x
Divided by 7
5x/7

5 times y, divided by 8

5 times y
5y
Divided by 8
5y/8

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]

50 is how many times as big as 20

50 is how many times as big as 20
50/20 = [B]2.5[/B]

6 times a number multiplied by 3 all divided by 4

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

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

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

6 times j squared minus twice j squared

6 times j squared minus twice j squared
j squared means we raise the variable j to the power of 2:
j^2
6 times j squared means we multiply j^2 by 6:
6j^2
Twice j squared means we multiply j^2 by 2:
2j^2
The word [I]minus[/I] means we subtract 2j^2 from 6j^2
6j^2 - 2j^2
So if you must simplify, we group like terms and get:
(6 - 2)j^2
[B]4j^2[/B]

6 times the quantity 17b minus 19

6 times the quantity 17b minus 19
the quantity 17b minus 19
17b - 19
6 times the quantity 17b minus 19
6(17b - 19)

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

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

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

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

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

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

6 times the sum of a number and 5 is 16

6 times the sum of a number and 5 is 16
A number represents an arbitrary variable, let's call it x
x
The sum of x and 5
x + 5
6 times the sum of x and 5
6(x + 5)
Is means equal to, so set 6(x + 5) equal to 16
[B]6(x + 5) = 16[/B]

6 times y divided by x squared

6 times y divided by x squared
6 times y:
6y
x squared means we raise x to the power of 2:
x^2
The phrase [I]divided by[/I] means we have a fraction:
[B]6y/x^2[/B]

6 times y divided by x squared

6 times y divided by x squared
6 times y:
6y
x squared means we raise x to the power of 2:
x^2
The phrase [I]divided by[/I] means we divide 6y by x^2:
[B]6y/x^2[/B]

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

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

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

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

67 less than the quantity 96 times q

67 less than the quantity 96 times q
96 times q:
96q
67 less than the quantity 96 times q
[B]96q - 67[/B]

7 bananas at 15˘ each

We have 15 cents times 7 bananas = $1.05

7 less than -2 times a number x is greater than or equal to 41

-2 times a number x is written as -2x.
Less means subtract, so we have 7 less than this is -2x - 7.
Finally, greater than or equal to is >=, so our expression becomes:
-2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41

-2 times a number x is denoted as -2x.
7 less than that means we subtract 7:
-2x - 7
Finally, that entire expression is greater than or equal to 41
-2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41

-2 times a number x is denoted as -2x.
7 less means we subtract, so 7 less than that is -2x - 7.
Finally, that entire expression is greater than or equal to 41
-2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41

7 less than -2 times a number x is greater than or equal to 41
-2 times a number x
-2x
7 less than this
-2x - 7
Now we set this expressions greater than or equal to 41
[B]-2x - 7 >= 41[/B]

7 times a number and 2 is equal to 4 times a number decreased by 8

7 times a number and 2 is equal to 4 times a number decreased by 8
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
7 times a number:
7x
and 2 means we add 2:
7x + 2
4 times a number
4x
decreased by 8 means we subtract 8:
4x - 8
The phrase [I]is equal to[/I] means an equation, so we set 7x + 2 equal to 4x - 8:
[B]7x + 2 = 4x - 8[/B]

7 times a number increased by 4 times the number

7 times a number increased by 4 times the number
Let [I]a number[/I] and [I]the number[/I] be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces:
[LIST]
[*]7 times a number: 7x
[*]4 times the number: 4x
[*]The phrase [I]increased by[/I] means we add 4x to 7x:
[*]7x + 4x
[*]Simplifying, we get: (7 + 4)x
[*][B]11x[/B]
[/LIST]

7 times a number is the same as 12 more than 3 times a number

7 times a number is the same as 12 more than 3 times a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[B][U]Algebraic Expression 1:[/U][/B]
7 times a number means we multiply 7 by x:
7x
[B][U]Algebraic Expression 2:[/U][/B]
3 times a number means we multiply 3 by x:
3x
12 more than 3 times a number means we add 12 to 3x:
3x + 12
The phrase [I]is the same as[/I] means an equation, so we set 7x equal to 3x + 12
[B]7x = 3x + 12[/B] <-- Algebraic Expression

7 times a positive number n is decreased by 3, it is less than 25

7 times a positive number n is decreased by 3, it is less than 25
7 times a positive number n:
7n
Decreased by 3:
7n - 3
The phrase [I]it is less than [/I]means an inequality. So we relate 7n - 3 less than 25 using the < sign to get our algebraic expression of:
[B]7n - 3 < 25[/B]

7 times the cube of the sum of x and 8

7 times the cube of the sum of x and 8
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The sum of x and 8 means we add 8 to x: x + 8
[*]The cube of this sum means we raise the sum to the 3rd power: (x + 8)^3
[*]7 times this cubed sum means we multiply (x + 8)^3 by 7:
[/LIST]
[B]7(x + 8)^3[/B]

7 times the number of lions plus 4 times the number of tigers

7 times the number of lions plus 4 times the number of tigers
Let the number of lions be l
Let the number of tigers be t
We have an algebraic expression of:
[B]7l + 4t[/B]

7 times the quantity of 3 times a number reduced by 10

7 times the quantity of 3 times a number reduced by 10
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
3 times a number:
3x
Reduced by 10 means we subtract 10:
3x - 10
7 times this quantity:
[B]7(3x - 10)[/B]

7 times the quantity of a plus b

7 times the quantity of a plus b
The quantity of a plus b:
a + b
7 times this quantity:
[B]7(a + b)[/B]

74 increased by 3 times y

74 increased by 3 times y
[U]3 times y[/U]
3y
[U]74 increased by 3 times y[/U]
[B]74 + 3y[/B]

78 times the quantity p minus 3

78 times the quantity p minus 3
The quantity p minus 3:
p - 3
78 times this quantity:
[B]78(p - 3)[/B]

8 times 4 plus m squared

8 times 4 plus m squared
m squared means we raise m to the power of 2
m^2
4 plus m squared:
4 + m^2
8 times 4 plus m squared
[B]8(4 + m^2)[/B]

8 times the difference of 5y and 3

8 times the difference of 5y and 3
The difference of 5y and 3 means we subtract 3 from 5y:
5y - 3
8 times the difference means we multiply (5y - 3) by 8:
[B]8(5y - 3)[/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 times the quantity x plus y

8 times the quantity x plus y
The quantity x plus y:
x + y
8 times the quantity:
[B]8(x + y)[/B]

8 times the sum of 5 times a number and 9

8 times the sum of 5 times a number and 9
Take this algebraic expression in parts:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
5 times a number means:
5x
The sum of this and 9 means we add 9 to 5x:
5x + 9
Now we multiply 8 times this sum:
[B]8(5x + 9)[/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 less than 5 times a number is 3 more than 2x

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

9 subtracted from the product of 3 and a number is greater than or equal to 16

9 subtracted from the product of 3 and a number is greater than or equal to 16
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The product of 3 and a number means we multiply 3 times x: 3x
[*]9 subtracted from the product: 3x - 9
[*]The phrase is greater than or equal to means an inequality. So we set up an inequality with >= for the greater than or equal to sign in relation to 3x - 9 and 16
[/LIST]
Our algebraic expression (inequality) becomes:
[B]3x - 19 >= 16[/B]

9 times a number is that number minus 10

9 times a number is that number minus 10
The phrase [I]a number[/I] means we define a random/arbitrary variable, let's call it x:
x
9 times a number means we multiply x by 9:
9x
The phrase [I]that number[/I] refers back to the original arbitrary variable we defined above, which is x:
x
That number minus 10 means we subtract 10 from x:
x - 10
The word [I]is[/I] means equal to, so we set 9x equal to x - 10
[B]9x = x - 10[/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 times x is twice the sum of x and 5

9 times x is twice the sum of x and 5
9 times x:
9x
the sum of x and 5
x + 5
twice the sum of x and 5
2(x + 5)
The phrase [I]is[/I] means equal to, so we set 9x equal to 2(x + 5)
[B]9x = 2(x + 5)[/B]

9 times x squared times y times z

9 times x squared times y times z
x squared:
x^2
x squared times y times z
x^2yz
9 times x squared times y times z
9x^2yz

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

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

A 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 bowler knocks down at least 6 pins 70 percent of the time. Out of 200 rolls, how many times can yo

A bowler knocks down at least 6 pins 70 percent of the time. Out of 200 rolls, how many times can you predict the bowler will knock down at least 6 pins?
Expected Value of (knocking down at least 6 pins) = number of rolls * probability of knocking down at least 6 pins
Expected Value of (knocking down at least 6 pins) = 200 * 0.7
Expected Value of (knocking down at least 6 pins) = [B]140[/B]

A business owner spent $4000 for a computer and software. For bookkeeping purposes, he needs to post

A business owner spent $4000 for a computer and software. For bookkeeping purposes, he needs to post the price of the computer and software separately. The computer costs 4 times as much as the software. What is the cost of the software?
Let c be the cost of the computer and s be the cost of the software. We have two equations:
[LIST=1]
[*]c + s = 4000
[*]c = 4s
[/LIST]
Substitute (2) into (1)
(4s) + s = 4000
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=4s%2Bs%3D4000&pl=Solve']equation solver[/URL], we get [B]s = 800[/B].
Substitute this into Equation (2), we get:
c = 4(800)
[B]c = 3,200[/B]

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

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

A certain culture of the bacterium Streptococcus A initially has 8 bacteria and is observed to doubl

A certain culture of the bacterium Streptococcus A initially has 8 bacteria and is observed to double every 1.5 hours.After how many hours will the bacteria count reach 10,000.
Set up the doubling times:
0 | 8
1.5 | 16
3 | 32
4.5 | 64
6 | 128
7.5 | 256
9 | 512
10.5 | 1024
12 | 2048
13.5 | 4096
15 | 8192
16.5 | 16384
So at time [B]16.5[/B], we cross 10,000 bacteria.

A classroom fish tank contains x goldfish. The tank contains 4 times as many guppies as goldfish. En

A classroom fish tank contains x goldfish. The tank contains 4 times as many guppies as goldfish. Enter an equation that represents the total number of guppies, y, in the fish tank.
The phrase [I]4 times as many[/I] means we multiply the goldfish (x) by 4 to get the number of guppies (y):
[B]y = 4x[/B]

A coffee franchise is opening a new store. The company estimates that there is a 75% chance the sto

A coffee franchise is opening a new store. The company estimates that there is a 75% chance the store will have a profit of $45,000, a 10% chance the store will break even, and a 15% chance the store will lose $2,500. Determine the expected gain or loss for this store.
Calculate the expected value E(x). Expected value is the sum of each event probability times the payoff or loss:
E(x) = 0.75(45,000) + 0.1(0) + 0.15(-2,500) <-- Note, break even means no profit and no loss and a loss is denoted with a negative sign
E(x) = 33,750 + 0 - 375
E(x) = [B]33,375 gain[/B]

A coin is tossed 3 times. a. Draw a tree diagram and list the sample space that shows all the possib

A coin is tossed 3 times. a. Draw a tree diagram and list the sample space that shows all the possible outcomes
[URL='https://www.mathcelebrity.com/cointoss.php?hts=+HTHTHH&hct=+2&tct=+1&fct=+5>=no+more+than&nmnl=+2&htpick=heads&tossct=3&montect=3&calc=5&pl=Calculate+Probability']type in "toss a coin 3 times" and pick the probability option[/URL].

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

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

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

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

A 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 credit plan charges interest rate of 36% compounded monthly. Find the effective rate.

A credit plan charges interest rate of 36% compounded monthly. Find the effective rate.
[U]Calculate Monthly Nominal Rate:[/U]
Monthly Nominal Rate = Annual Rate / 12 months per year
Monthly Nominal Rate = 36%/12
Monthly Nominal Rate = 3%
[U]Since there are 12 months in a year, we compound 12 times to get the effective rate below:[/U]
Effective Rate = (1 + Monthly Nominal Rate as a Decimal)^12 - 1
Since 3% = 0.03, we have:
Effective Rate = 100% * ((1 + 0.03)^12 - 1)
Effective Rate = 100% * ((1.03)^12 - 1)
Effective Rate = 100% * (1.42576088685 - 1)
Effective Rate = 100% * (0.42576088685)
Effective Rate = [B]42.58%[/B]

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle?

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle?
Area of a cube is length times width:
A = 8 & 3/4 * 6 & 1/2
We need to convert these to improper fractions.
[LIST]
[*]8 & 3/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%263%2F4&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 35/4
[*]6 & 1/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%261%2F2&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 13/2
[/LIST]
Multiply the improper fractions together:
A = 35/4 * 13/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=35%2F4&frac2=13%2F2&pl=Multiply']Using our fraction multiplier[/URL], we get:
[B]455/8 sq ft[/B]
If you want to convert this to a mixed fraction, we [URL='https://www.mathcelebrity.com/fraction.php?frac1=455%2F8&frac2=3%2F8&pl=Simplify']type this in our calculator [/URL]and get:
[B]56 & 7/8 sq ft[/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 faucet drips 15 milliliters of water every 45 minutes. How many milliliters of water will it drip

A faucet drips 15 milliliters of water every 45 minutes. How many milliliters of water will it drip in 3 hours?
3 hours = 60 * 3 = 180 minutes
180 minutes / 45 minutes = 4
So the faucet drips 15 milliliters 4 times
15 * 4 = [B]60 milliliters[/B]

A furniture company plans to have 25 employees at its corporate headquarters and 25 employees at eac

A furniture company plans to have 25 employees at its corporate headquarters and 25 employees at each store it opens. Let s represent the number of stores and m represent the total number of employees.
There is only one corporate headquarters. So we have the number of employees (m) as:
m = Store Employees + Corporate Employees
Each store has 25 employees. Total store employees equal 25 per store times the number of stores (s).
[B]m = 25s + 25[/B]

A garden has a length that is three times its width. If the width is n feet and fencing cost $8 per

A garden has a length that is three times its width. If the width is n feet and fencing cost $8 per foot, what is the cost of the fencing for the garden?
Garden is a rectangle which has Perimeter P of:
P = 2l + 2w
l = 3w
P = 2(3w) + 2w
P = 6w + 2w
P = 8w
Width w = n, so we have:
P = 8n
Cost = 8n * 8 = [B]64n dollars[/B]

A group of 30 students from your school is part of the audience for a TV game show. The total number

A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience is 120. What theoretical probability of 5 students from your school being selected as contestants out of 9 possible contestant spots?
We want the probability a student from your school is chosen out of total students times total ways to choose students from your school:
[U]a) P(5 students being selected):[/U]
5/30 * 4/(120 - 30)
5/30 * 4/90
20/2700
[URL='https://www.mathcelebrity.com/fraction.php?frac1=20%2F2700&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get:
1/135
[U]b) Total Ways 9 students can be picked from your school:[/U]
9/120
[URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F120&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get:
3/40
Divide a by b:
1/135 / 3/40
40/405
[URL='https://www.mathcelebrity.com/fraction.php?frac1=40%2F405&frac2=3%2F8&pl=Simplify']Simplifying[/URL], we get:
[B]8/81[/B]

A group of people was surveyed to determine what newspaper they read. 80% of those interviewed read

A group of people was surveyed to determine what newspaper they read. 80% of those interviewed read the New York Times, while 50% read U.S.A. Today. If 35% read both papers, what percent read neither paper?
New York Times:
80% - 35% for both = 45%
USA Today:
50% - 35% for both = 15%
45% + 15% + 35% = 95%
Which means 100% - 95% = [B]5% read neither[/B]

A gym has yoga classes. Each class has 11 students. If there are c classes, write an equation to rep

A gym has yoga classes. Each class has 11 students. If there are c classes, write an equation to represent the total number of students s taking yoga.
Total students is the number of classes times the number of students in each class:
[B]s = 11c[/B]

A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 2

A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 20 feet less than 3 times the width, what are the dimensions of the rectangular plot?
[U]Set up equations:[/U]
(1) 2l + 2w = 800
(2) l = 3w - 20
[U]Substitute (2) into (1)[/U]
2(3w - 20) + 2w = 800
6w - 40 + 2w = 800
[U]Group the w terms[/U]
8w - 40 = 800
[U]Add 40 to each side[/U]
8w = 840
[U]Divide each side by 8[/U]
[B]w = 105
[/B]
[U]Substitute w = 105 into (2)[/U]
l = 3(105) - 20
l = 315 - 20
[B]l = 295[/B]

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

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

A house costs 3.5 times as much as the lot. Together they sold for $135,000. Find the cost of each

A house costs 3.5 times as much as the lot. Together they sold for $135,000. Find the cost of each.
Let the house cost be h, and the lot cost be l. We have the following equations:
[LIST=1]
[*]h = 3.5l
[*]h + l = 135,000
[/LIST]
Substitute (1) into (2)
3.5l + l = 135,000
Combine like terms:
4.5l = 135,000
Divide each side by 4.5 to isolate l
[B]l = 30,000[/B]
Substitute this back into equation (1)
h = 3.5(30,000)
[B]h = 105,000[/B]

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

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

A man is four times as old as his son. In five years time he will be three times as old. Find their

A man is four times as old as his son. In five years time he will be three times as old. Find their present ages.
Let the man's age be m, and the son's age be s. We have:
[LIST=1]
[*]m = 4s
[*]m + 5 = 3(s + 5)
[/LIST]
Substitute (1) into (2)
4s + 5 = 3s + 15
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=4s%2B5%3D3s%2B15&pl=Solve']equation calculator[/URL], and we get [B]s = 10[/B].
m = 4(10)
[B]m = 40[/B]

A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of

A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight.
Every month, the baby gains 2/3 of a pound. So we have:
[B]y = 2/3x + 7
[/B]
The baby starts off with 7 pounds. So we add 7 pounds + 2/3 times the number of months passed since birth.

A person invests $500 in an account that earns a nominal yearly rate of 4%. How much will this inves

A person invests $500 in an account that earns a nominal yearly rate of 4%. How much will this investment be worth in 10 years? If the interest was applied four times per year (known as quarterly compounding), calculate how much the investment would be worth after 10 years.
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=500&nval=10&int=4&pl=Annually']compound interest calculator[/URL], $500 @ 4% for 10 years is:
$[B]740.12
[/B]
Using [URL='https://www.mathcelebrity.com/compoundint.php?bal=500&nval=40&int=4&pl=Quarterly']quarterly compounding in our compound interest calculator[/URL], we have 10 years * 4 quarters per year = 40 periods, so we have:
[B]$744.43[/B]

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

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

A private jet flies the same distance in 4 hours that a commercial jet flies in 2 hours. If the spee

A private jet flies the same distance in 4 hours that a commercial jet flies in 2 hours. If the speed of the commercial jet was 154 mph less than 3 times the speed of the private jet, find the speed of each jet.
Let p = private jet speed and c = commercial jet speed. We have two equations:
(1) c = 3p - 154
(2) 4p =2c
Plug (1) into (2):
4p = 2(3p - 154)
4p = 6p - 308
Subtract 4p from each side:
2p - 308 = 0
Add 308 to each side:
2p = 308
Divide each side by 2:
[B]p = 154[/B]
Substitute this into (1)
c = 3(154) - 154
c = 462 - 154
[B]c = 308[/B]

A random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afte

A random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes).
Checkout Time (in minutes) | Frequency | Relative Frequency
1.0 - 1.9 | 2 | ?
2.0 - 2.9 | 8 | ?
3.0 - 3.9 | ? | ?
4.0 - 5.9 | 5 | ?
Total | 25 | ?
(a) Complete the frequency table with frequency and relative frequency.
(b) What percentage of the checkout times was less than 3 minutes?
(c)In what class interval must the median lie? Explain your answer.
(d) Assume that the largest observation in this dataset is 5.8. Suppose this observation were incorrectly recorded as 8.5 instead of 5.8. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Why?
(a)
[B]Checkout Time (in minutes) | Frequency | Relative Frequency
1.0 - 1.9 | 2 | 2/25
2.0 - 2.9 | 8 | 8/25
3.0 - 3.9 | 10 (since 25 - 5 + 8 + 2) = 10 | 10/25
4.0 - 5.9 | 5 | 5/25
Total | 25 | ?[/B]
(b) (2 + 8)/25 = 10/25 = [B]40%[/B]
c) [B]3.0 - 3.9[/B] since 2 + 8 + 10 + 5 = 25 and 13 is the middle value which occurs in the 3.0 - 3.9 interval
(d) [B]Mean increases[/B] since it's a higher value than usual. Median would not change as the median is the most frequent distribution and assuming the 5.8 is only recorded once.

A random sample of STAT200 weekly study times in hours is as follows: 2 15 15 18 30 Find the sam

A random sample of STAT200 weekly study times in hours is as follows: 2 15 15 18 30 Find the sample standard deviation. (Round the answer to two decimal places. Show all work.)
[B]9.98[/B] using [URL='http://www.mathcelebrity.com/statbasic.php?num1=+2,15,15,18,30&num2=+0.2,0.4,0.6,0.8,0.9&pl=Number+Set+Basics']our standard deviation calculator[/URL]

A rectangle has a length that is 8.5 times its width. IF the width is n, what is the perimeter of th

A rectangle has a length that is 8.5 times its width. IF the width is n, what is the perimeter of the rectangle.
w = n
l = 8.5n
P = 2(8.5n) + 2n
P = 17n + 2n
P = [B]19n[/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 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 restaurant chain sells 15,000 pizzas each month, and 70% of the pizzas are topped with pepperoni.

A restaurant chain sells 15,000 pizzas each month, and 70% of the pizzas are topped with pepperoni. Of these, 2/3 also have peppers. How many pizzas have pepperoni and peppers?
We multiply the pizzas sold by the percentage of pepperoni times the fraction of peppers. Since 70% is 7/10, we have:
Pizzas with pepperoni and peppers = 15,000 * 7/10 * 2/3
7/10 * 2/3 = 14/30. [URL='https://www.mathcelebrity.com/fraction.php?frac1=14%2F30&frac2=3%2F8&pl=Simplify']Using our fraction simplifier calculator[/URL], we can reduce this to 7/15
Pizzas with pepperoni and peppers = 15,000 * 7/15
Pizzas with pepperoni and peppers = [B]7,000[/B]

A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment

A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $584. What was the simple interest rate of the bonds?
For simple interest, we have:
Balance * interest rate = Interest payment
8000i = 584
Divide each side of the equation by 8000 to isolate i:
8000i/8000 = 584/8000
Cancelling the 8000's on the left side, we get:
i = 0.073
Most times, interest rates are expressed as a percentage.
Percentage interest = Decimal interest * 100%
Percentage interest = 0.073 * 100%
Multiplying by 100 is the same as moving the decimal point two places right:
Percentage interest = [B]7.3%[/B]

A shirt costs 15 and jeans costs 25. write an expressions for the costs of j jeans and s shirts

A shirt costs 15 and jeans costs 25. write an expressions for the costs of j jeans and s shirts.
Cost equals quantity times price, so we have the total cost C:
[B]C(s, j) = 15s + 25j[/B]

A street sign is 85 inches tall. How tall is it in feet and inches?

A street sign is 85 inches tall. How tall is it in feet and inches?
Since 12 inches is a foot, we have:
12 goes into 85 7 times remainder 1
So we have [B]7 feet, 1 inch[/B]

A submarine at an elevation of -185 meters descends to 3 times that elevation. Then, it elevates 90

A submarine at an elevation of -185 meters descends to 3 times that elevation. Then, it elevates 90 meters. What is the submarines new elevation?
3 times the current elevation is:
3 * -185 = -555
Elevating 90 meters means we have a positive change:
-555 + 90 = [B]-465[/B]

A suitcase contains nickels, dimes and quarters. There are 2&1/2 times as many dimes as nickels and

A suitcase contains nickels, dimes and quarters. There are 2&1/2 times as many dimes as nickels and 5 times the number of quarters as the number of nickels. If the coins have a value of $24.80, how many nickels are there in the suitcase?
Setup number of coins:
[LIST]
[*]Number of nickels = n
[*]Number of dimes = 2.5n
[*]Number of quarters = 5n
[/LIST]
Setup value of coins:
[LIST]
[*]Value of nickels = 0.05n
[*]Value of dimes = 2.5 * 0.1n = 0.25n
[*]Value of quarters = 5 * 0.25n = 1.25n
[/LIST]
Add them up:
0.05n + 0.25n + 1.25n = 24.80
Solve for [I]n[/I] in the equation 0.05n + 0.25n + 1.25n = 24.80
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(0.05 + 0.25 + 1.25)n = 1.55n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
1.55n = + 24.8
[SIZE=5][B]Step 3: Divide each side of the equation by 1.55[/B][/SIZE]
1.55n/1.55 = 24.80/1.55
n = [B]16[/B]
[B]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05n%2B0.25n%2B1.25n%3D24.80&pl=Solve']Source[/URL][/B]

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

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

a times b divided by the quantity a minus b

a times b divided by the quantity a minus b
a times b:
ab
a minus b:
a - b
Now divide a times b by a minus b:
[B]ab/(a - b)[/B]

A times r squared multiplied by h

A times r squared multiplied by h
r squared means we raise r to the power of 2:
r^2
a times r squared:
ar^2
Multiplied by h:
[B]ahr^2[/B]

A towns population is currently 500. If the population doubles every 30 years, what will the populat

A towns population is currently 500. If the population doubles every 30 years, what will the population be 120 years from now?
Find the number of doubling times:
120 years / 30 years per doubling = 4 doubling times
Set up our growth function P(n) where n is the number of doubling times:
P(n) = 500 * 2^n
Since we have 4 doubling times, we want P(4):
P(4) = 500 * 2^4
P(4) = 500 * 16
P(4) = [B]8,000[/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 woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and

A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and walked back to the starting point along the same path. She walks 4mph on level ground, 3 mph uphill, and 6 mph downhill. Find the distance she walked.
Hint: Think about d = rt, which means that t = d/r. Think about each section of her walk, what is the distance and the rate. You know that the total time is 5 hours, so you know the sum of the times from each section must be 5.
Let Level distance = L and hill distance = H. Add the times it took for each section of the walk:
L/4 + H /3 + H/6 + L/4 = 5
The LCD of this is 12 from our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=3&num3=6&pl=LCM']LCD Calculator[/URL]
[U]Multiply each side through by our LCD of 12[/U]
3L + 4H + 2H + 3L = 60
[U]Combine like terms:[/U]
6L + 6H = 60
[U]Divide each side by 3:[/U]
2L + 2H = 20
The woman walked [B]20 miles[/B]

A young snake measures 0.23 meters long. During the course of his lifetime,he will grow to be 13 tim

A young snake measures 0.23 meters long. During the course of his lifetime,he will grow to be 13 times his current length what will be his length be when he is full grown
Full Grown Length = Current Length * Growth Multiplier
Full Grown Length = 0.23 * 13
Full Grown Length = [B]2.99 meters[/B]

a ^5 x a ^2 without exponents

a ^5 x a ^2 without exponents
When we multiply the same variable or number, we add exponents, so we have:
a^(5 + 2)
a^7
To write a variable raised to an exponent without exponents, we break it up. The formula to do this is:
a^n = a times itself n times
a^7 = [B]a * a * a * a * a * a * a[/B]

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applie

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional onetime untaxed fee of $5.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying [I]x[/I] nights?
[LIST]
[*]The Room cost equals 99.95 times x where x is the number of rooms
[*]We express an 8% tax by multiplying the room cost by 1.08
[*]Finally, we add on $5, which is [I]untaxed[/I]
[/LIST]
[I][/I]
Take this in pieces:
Room Cost: 99.95x
Tax on Room 1.08(99.95x)
Add on $5 which is untaxed: [B]1.08(99.95x) + 5[/B]

add 6 to 2 times c

[U]2 times c[/U]
2c
[U]Add 6[/U]
[B]2c + 6[/B]

add s and t, multiply the result by u, then add r to what you have

add s and t, multiply the result by u, then add r to what you have.
Take this algebraic expression in 3 parts:
[LIST=1]
[*]Add s and t: s + t
[*]Multiply the result by u means me multiply (s + t) times u: u(s + t)
[*]Then add r to what you have. [I]what you have means the result in #2.[/I]
[/LIST]
[B]u(s + t) + r[/B]

Admir works at a coffee shop and earns $9/hour he also works at a grocery store and earns $15/hour.

Admir works at a coffee shop and earns $9/hour he also works at a grocery store and earns $15/hour. Last week he earned $500 dollars. Write an equation that represents the situation.
[LIST]
[*]Let c be the hours Admir works at the coffee shop.
[*]Let g be the hours Admir works at the grocery store.
[/LIST]
Since earnings equal hourly rate times hours, We have the following equation:
[B]9c + 15g = 500[/B]

Age now and then

I brute forced this and got a wrong answer, logic tells me is right. I tried the calculator here but maybe messed up the equation using another users problem as an example. Having no luck.
Problem:
Jacob is 4 times the age of Clinton. 8 years ago Jacob was 9 times the age of Clinton. How old are they now and how old were they 8 years ago?

Age now and then

Thank you, but I'm going to have to talk to my teacher about how someone can't be 9 times older than nothing....

Age now and then

I read it wrong before. Here you go:
Jacob is 4 times the age of Clinton. 8 years ago Jacob was 10 times the age of Clinton. How old are they now and how old were they 8 years ago?
[LIST=1]
[*]j = 4c
[*]j - 8 = 10(c - 8)
[/LIST]
Substitute (1) into (2)
(4c) - 8 = 10c - 80
[URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D10c-80&pl=Solve']Equation solver[/URL] gives us [B]c = 12[/B] which means j = 4(12) = [B]48[/B].
8 years ago,[B] j = 40 and c = 4[/B] which holds the 10x rule.

Age now and then

[QUOTE="math_celebrity, post: 1163, member: 1"]I read it wrong before. Here you go:
Jacob is 4 times the age of Clinton. 8 years ago Jacob was 10 times the age of Clinton. How old are they now and how old were they 8 years ago?
[LIST=1]
[*]j = 4c
[*]j - 8 = 10(c - 8)
[/LIST]
Substitute (1) into (2)
(4c) - 8 = 10c - 80
[URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D10c-80&pl=Solve']Equation solver[/URL] gives us [B]c = 12[/B] which means j = 4(12) = [B]48[/B].
8 years ago,[B] j = 40 and c = 4[/B] which holds the 10x rule.[/QUOTE]
Thank you, I see what I did wrong!

Age now problems

The age of the older of the two boys is twice that of the younger. 5 years ago it was three times that of the younger. Find the age of each

Age now problems

A father is three times as old as the son, and the daughter is 3 years younger than the son. If the sum of their ages 3 years ago was 63
Find the present age of the father

Alberto’s salary was $1500 greater than 5 times Nick’s salary. Write an equation stating Alberto’s a

Alberto’s salary was $1500 greater than 5 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y.
Let x be Alberto's salary. Let y be Nick's salary. We have:
Let's break this down:
[LIST=1]
[*]5 times Nick's salary (y), means we multiply the variable y by 5
[*]$1500 greater means we add $1500 to 5y
[/LIST]
[B]x = 5y - 1500[/B]

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s a

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y.
If Alberto's salary is x and Nick's salary is y, we have:
[B]x = 4y + 2000[/B]

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s a

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y.
Let Alberto's salary be x, and Nick's salary be y.
We have:
[B]x = 4y + 2000[/B]

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s a

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y.
If Alberto's salary is x and Nick's is y, we have:
[B]x = 4y + 2000 [/B](since greater than means we add)

Algebraic Expressions

This calculator builds algebraic expressions based on word representations of numbers using the four operators and the words that represent them(increased,product,decreased,divided,times)
Also known as Mathematical phrases

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]

An airport has 13 scheduled arrivals every day. This week, 28 private planes also landed there. How

An airport has 13 scheduled arrivals every day. This week, 28 private planes also landed there. How many planes flew into the airport this week?
A week has 7 days.
13 scheduled arrivals per day times 7 days = 91 scheduled planes
Next, we add 28 private planes:
91 + 28 = [B]119 planes[/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 eccentric millionaire decided to give away $1,000,000 if Janelle took one die and rolled a "4". H

An eccentric millionaire decided to give away $1,000,000 if Janelle took one die and rolled a "4". He wanted Janelle to have a better than 1 in 6 chance of winning, so before she rolled the die he told her that she could roll the die 3 times. If any roll was a "4", she would win the million dollars. What are Janelle's chances of winning the million dollars?
Chance of winning each roll is 1/6. Which means the chances of losing each roll are 1 - 1/6 = 5/6
Calculate the probability of 3 straight losing rolls:
P(Lose) = P(Loser) * P(Loser) * P(Loser) = 5/6 * 5/6 * 5/6 = 125/216
P(Win) = 1 - P(Lose)
P(Win) = 1 - 125/216
P(Win) = 216/216 -125/216
P(Win) = [B]91/216[/B]

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

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

An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three tim

An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three times as long as the shortest side. The remaining two sides are each 8m longer than the shortest side. The perimeter of the Pentagon is 79m. Find the length of each side of the Pentagon.
Let long sides be l. Let short sides be s. Let medium sides be m. We have 3 equations:
[LIST=1]
[*]2l + 2m + s = 79
[*]m = s + 8
[*]l = 3s
[/LIST]
Substitute (2) and (3) into (1):
2(3s) + 2(s + 8) + s = 79
Multiply through and simplify:
6s + 2s + 16 + s = 79
9s + 16 = 79
[URL='https://www.mathcelebrity.com/1unk.php?num=9s%2B16%3D79&pl=Solve']Using our equation calculator[/URL], we get [B]s = 7[/B].
This means from Equation (2):
m = 7 + 8
[B]m = 15
[/B]
And from equation (3):
l = 3(7)
[B]l = 21[/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]

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]

Anna is collecting boxes of cereal to deliver in a food bank. The volume of each cereal box is 324 c

Anna is collecting boxes of cereal to deliver in a food bank. The volume of each cereal box is 324 cubic inches. The picture shows the cereal boxes she has collected so far. A large delivery box holds three times as many boxes as Anna collected.
About what is the volume of the delivery box?
The picture has 12 cereal boxes. Since the delivery box holds three times as many cereal boxes as Anna collected, the delivery box holds 12 * 3 = 36 cereal boxes.
With each cereal box having a volume of 324 cubic inches, we have the total volume as:
V = 324 cubic inches * 36 cereal boxes
V = [B]11,664 cubic inches[/B]

Anna’s age increased by 3 times her age, the result is 72

Anna’s age increased by 3 times her age, the result is 72.
Let a be Anna's age. We have:
a + 3a = 72
Combine like terms:
(1 + 3)a = 72
4a = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=4a%3D72&pl=Solve']Type 4a = 72 into our calculator[/URL], and we get [B]a = 18[/B].

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

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

Ashley deposited $4000 into an account with 2.5% interest, compounded semiannually. Assuming that no

Ashley deposited $4000 into an account with 2.5% interest, compounded semiannually. Assuming that no withdrawals are made, how much will she have in the account after 10 years?
Semiannual means twice a year, so 10 years * 2 times per year = 20 periods. We use this and [URL='https://www.mathcelebrity.com/compoundint.php?bal=4000&nval=20&int=2.50&pl=Semi-Annually']plug the numbers into our compound interest calculator[/URL] to get:
[B]$5,128.15[/B]

at a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2.

at a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2.
[LIST]
[*]How many men at the party?
[*]How many ladies at the party?
[*]How many kids at the party?
[/LIST]
Our total ratio denominator is 4 + 3 + 2 = 9. To find the number of each type of person, we take their ratio divided by their ratio numerator times 72 people at the party
[U]Calculate ratios:[/U]
[LIST]
[*]Men: [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F9&frac2=72&pl=Multiply']4/9 * 72[/URL] = [B]32[/B]
[*]Ladies: [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F9&frac2=72&pl=Multiply']3/9 * 72[/URL] = [B]24[/B]
[*]Kids: [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F9&frac2=72&pl=Multiply']2/9 * 72[/URL] = [B]16[/B]
[/LIST]
[U]Check our work:[/U]
Men + Ladies + Kids = 32 + 24 + 16
Men + Ladies + Kids = 72 <-- This checks out!

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]

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]

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]

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

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

C times the product b and a

C times the product b and a
[U]The product b and a:[/U]
ab
[U]c times the product:[/U]
[B]abc[/B]

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

Clock Angle

Calculate the angle on a clock between the hour and minute hands or how many times on the clock form an angle of (x°) between the minute and hour hand (backwards and forwards). Clock Angle Calculator

Committees of 4 men 5 women form a group of 11 men and 11 women.

Committees of 4 men 5 women form a group of 11 men and 11 women.
We want combinations.
4 men from 11 men is the combination 11C4. [URL='https://www.mathcelebrity.com/permutation.php?num=11&den=4&pl=Combinations']Using our combinations calculator[/URL], we get:
11C4 = 330
5 women from 11 women is the combination 11C5. [URL='https://www.mathcelebrity.com/permutation.php?num=11&den=5&pl=Combinations']Using our combinations calculator[/URL], we get:
11C5 = 462
We multiply the committee of men times the committee of women:
11C4 * 11C5 = 330 * 432
11C4 * 11C5 = [B]142,560[/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]

Corvettes are known as sporty cars that can travel at high rates of speed. It is therefore assumed t

Corvettes are known as sporty cars that can travel at high rates of speed. It is therefore assumed that they are much more dangerous than minivans. An owner of a Corvette points out that when statistics are studied, there are far more deaths each year from crashes that involve minivans than crashes that involve Corvettes, so Corvettes, so Corvettes must be safer than minivans. The statistics the Covert owner sites are correct. Is his logic faulty? Why or why not?
[B]Faulty.[/B]
There are hundreds of times more minivans on the road than Corvettes, so we expect more deaths even if they are the safest car on the road.

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]

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

Currently 16 out of every 25 American adults drink coffee every day. In a town with a population of

Currently 16 out of every 25 American adults drink coffee every day. In a town with a population of 7900 adults, how many of these adults would you expect to drink coffee ever
We'd multiply 16/25 times 7900:
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=7900&frac2=16/25&pl=Multiply']fraction multiplication calculator by type 16/25 of 7900[/URL], we get:
[B]5056[/B]

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

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

devaughn,sageis2timessydneysage,thesumoftheiragesis78,whatissydneysage

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

Erin has 72 stamps in her stamp drawer along with a quarter, two dimes and seven pennies. She has 3

Erin has 72 stamps in her stamp drawer along with a quarter, two dimes and seven pennies. She has 3 times as many 3-cent stamps as 37-cent stamps and half the number of 5-cent stamps as 37-cent stamps. The value of the stamps and coins is $8.28. How many 37-cent stamps does Erin have?
Number of stamps:
[LIST]
[*]Number of 37 cent stamps = s
[*]Number of 3-cent stamps = 3s
[*]Number of 5-cent stamps = 0.5s
[/LIST]
Value of stamps and coins:
[LIST]
[*]37 cent stamps = 0.37s
[*]3-cent stamps = 3 * 0.03 = 0.09s
[*]5-cent stamps = 0.5 * 0.05s = 0.025s
[*]Quarter, 2 dime, 7 pennies = 0.52
[/LIST]
Add them up:
0.37s + 0.09s + 0.025s + 0.52 = 8.28
Solve for [I]s[/I] in the equation 0.37s + 0.09s + 0.025s + 0.52 = 8.28
[SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE]
(0.37 + 0.09 + 0.025)s = 0.485s
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
0.485s + 0.52 = + 8.28
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 0.52 and 8.28. To do that, we subtract 0.52 from both sides
0.485s + 0.52 - 0.52 = 8.28 - 0.52
[SIZE=5][B]Step 4: Cancel 0.52 on the left side:[/B][/SIZE]
0.485s = 7.76
[SIZE=5][B]Step 5: Divide each side of the equation by 0.485[/B][/SIZE]
0.485s/0.485 = 7.76/0.485
s = [B]16[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.37s%2B0.09s%2B0.025s%2B0.52%3D8.28&pl=Solve']Source[/URL]

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 3 consecutive integers such that the sum of twice the smallest and 3 times the largest is 126

Find 3 consecutive integers such that the sum of twice the smallest and 3 times the largest is 126.
Let the first integer be n, the second integer be n + 1, and the third integer be n + 2. We have:
Sum of the smallest and 3 times the largest is 126:
n + 3(n + 2) = 126
Multiply through:
n + 3n + 6 = 126
Group like terms:
4n + 6 = 126
[URL='https://www.mathcelebrity.com/1unk.php?num=4n%2B6%3D126&pl=Solve']Type 4n + 6 = 126 into our calculator[/URL], we get n = 30. Which means the next two integers are 31 and 32.
[B]{30, 31, 32}[/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]

Finn has 8 toy cars. Dirk has t times as many toy cars as Finn

Finn has 8 toy cars. Dirk has t times as many toy cars as Finn
The phrase [I]times as many [/I]means we multiply:
[B]8t[/B]

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

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

Forward Rate

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

g equals 232 subtracted from the quantity 377 times g

g equals 232 subtracted from the quantity 377 times g
377 times g:
377g
232 subtracted from 377 times g:
377g - 232
We set the variable g equal to this expression:
[B]g = 377g - 232[/B]

g times by 5 then add 3

g times by 5 then add 3
The phrase [I]times by [/I]means times or multiplied by:
5g
Then add 3 means we add 3 to 5g:
[B]5g + 3
[MEDIA=youtube]7KeEWSY1WMg[/MEDIA][/B]

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

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

Hanna cooked 5 pizzas. She sliced each pizza into eighths. How many slices of pizza does she have in

Hanna cooked 5 pizzas. She sliced each pizza into eighths. How many slices of pizza does she have in total?
5 pizzas times 8 slices per pizza = [B]40 slices[/B]

Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts,

Practical Explanation ( For Example ) :- `1st of all can you tell me every single seconds detail from that time when you born ?? ( i need every seconds detail ?? that what- what you have thought and done on every single second )
can you tell me every single detail of your `1 cheapest Minute Or your whole hour, day, week, month, year or your whole life ??
if you are not able to tell me about this life then what proof do you have that you didn't forget your past ? and that you will not forget this present life in the future ?
that is Fact that Supreme Lord Krishna exists but we posses no such intelligence to understand him.
there is also next life. and i already proved you that no scientist, no politician, no so-called intelligent man in this world is able to understand this Truth. cuz they are imagining. and you cannot imagine what is god, who is god, what is after life etc.
_______
for example :Your father existed before your birth. you cannot say that before your birth your father don,t exists.
So you have to ask from mother, "Who is my father?" And if she says, "This gentleman is your father," then it is all right. It is easy.
Otherwise, if you makes research, "Who is my father?" go on searching for life; you'll never find your father.
( now maybe...maybe you will say that i will search my father from D.N.A, or i will prove it by photo's, or many other thing's which i will get from my mother and prove it that who is my Real father.{ So you have to believe the authority. who is that authority ? she is your mother. you cannot claim of any photo's, D.N.A or many other things without authority ( or ur mother ).
if you will show D.N.A, photo's, and many other proofs from other women then your mother. then what is use of those proofs ??} )
same you have to follow real authority. "Whatever You have spoken, I accept it," Then there is no difficulty. And You are accepted by Devala, Narada, Vyasa, and You are speaking Yourself, and later on, all the acaryas have accepted. Then I'll follow.
I'll have to follow great personalities. The same reason mother says, this gentleman is my father. That's all. Finish business. Where is the necessity of making research? All authorities accept Krsna, the Supreme Personality of Godhead. You accept it; then your searching after God is finished.
Why should you waste your time?
_______
all that is you need is to hear from authority ( same like mother ). and i heard this truth from authority " Srila Prabhupada " he is my spiritual master.
im not talking these all things from my own.
___________
in this world no `1 can be Peace full. this is all along Fact.
cuz we all are suffering in this world 4 Problems which are Disease, Old age, Death, and Birth after Birth.
tell me are you really happy ?? you can,t be happy if you will ignore these 4 main problem. then still you will be Forced by Nature.
___________________
if you really want to be happy then follow these 6 Things which are No illicit s.ex, No g.ambling, No d.rugs ( No tea & coffee ), No meat-eating ( No onion & garlic's )
5th thing is whatever you eat `1st offer it to Supreme Lord Krishna. ( if you know it what is Guru parama-para then offer them food not direct Supreme Lord Krishna )
and 6th " Main Thing " is you have to Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare ".
_______________________________
If your not able to follow these 4 things no illicit s.ex, no g.ambling, no d.rugs, no meat-eating then don,t worry but chanting of this holy name ( Hare Krishna Maha-Mantra ) is very-very and very important.
Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare " and be happy.
if you still don,t believe on me then chant any other name for 5 Min's and chant this holy name for 5 Min's and you will see effect. i promise you it works And chanting at least 16 rounds ( each round of 108 beads ) of the Hare Krishna maha-mantra daily.
____________
Here is no Question of Holy Books quotes, Personal Experiences, Faith or Belief. i accept that Sometimes Faith is also Blind. Here is already Practical explanation which already proved that every`1 else in this world is nothing more then Busy Foolish and totally idiot.
_________________________
Source(s):
every `1 is already Blind in this world and if you will follow another Blind then you both will fall in hole. so try to follow that person who have Spiritual Eyes who can Guide you on Actual Right Path. ( my Authority & Guide is my Spiritual Master " Srila Prabhupada " )
_____________
if you want to see Actual Purpose of human life then see this link : ( triple w ( d . o . t ) asitis ( d . o . t ) c . o . m {Bookmark it })
read it complete. ( i promise only readers of this book that they { he/she } will get every single answer which they want to know about why im in this material world, who im, what will happen after this life, what is best thing which will make Human Life Perfect, and what is perfection of Human Life. ) purpose of human life is not to live like animal cuz every`1 at present time doing 4 thing which are sleeping, eating, s.ex & fear. purpose of human life is to become freed from Birth after birth, Old Age, Disease, and Death.

Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts,

Practical Explanation ( For Example ) :- `1st of all can you tell me every single seconds detail from that time when you born ?? ( i need every seconds detail ?? that what- what you have thought and done on every single second )
can you tell me every single detail of your `1 cheapest Minute Or your whole hour, day, week, month, year or your whole life ??
if you are not able to tell me about this life then what proof do you have that you didn't forget your past ? and that you will not forget this present life in the future ?
that is Fact that Supreme Lord Krishna exists but we posses no such intelligence to understand him.
there is also next life. and i already proved you that no scientist, no politician, no so-called intelligent man in this world is able to understand this Truth. cuz they are imagining. and you cannot imagine what is god, who is god, what is after life etc.
_______
for example :Your father existed before your birth. you cannot say that before your birth your father don,t exists.
So you have to ask from mother, "Who is my father?" And if she says, "This gentleman is your father," then it is all right. It is easy.
Otherwise, if you makes research, "Who is my father?" go on searching for life; you'll never find your father.
( now maybe...maybe you will say that i will search my father from D.N.A, or i will prove it by photo's, or many other thing's which i will get from my mother and prove it that who is my Real father.{ So you have to believe the authority. who is that authority ? she is your mother. you cannot claim of any photo's, D.N.A or many other things without authority ( or ur mother ).
if you will show D.N.A, photo's, and many other proofs from other women then your mother. then what is use of those proofs ??} )
same you have to follow real authority. "Whatever You have spoken, I accept it," Then there is no difficulty. And You are accepted by Devala, Narada, Vyasa, and You are speaking Yourself, and later on, all the acaryas have accepted. Then I'll follow.
I'll have to follow great personalities. The same reason mother says, this gentleman is my father. That's all. Finish business. Where is the necessity of making research? All authorities accept Krsna, the Supreme Personality of Godhead. You accept it; then your searching after God is finished.
Why should you waste your time?
_______
all that is you need is to hear from authority ( same like mother ). and i heard this truth from authority " Srila Prabhupada " he is my spiritual master.
im not talking these all things from my own.
___________
in this world no `1 can be Peace full. this is all along Fact.
cuz we all are suffering in this world 4 Problems which are Disease, Old age, Death, and Birth after Birth.
tell me are you really happy ?? you can,t be happy if you will ignore these 4 main problem. then still you will be Forced by Nature.
___________________
if you really want to be happy then follow these 6 Things which are No illicit s.ex, No g.ambling, No d.rugs ( No tea & coffee ), No meat-eating ( No onion & garlic's )
5th thing is whatever you eat `1st offer it to Supreme Lord Krishna. ( if you know it what is Guru parama-para then offer them food not direct Supreme Lord Krishna )
and 6th " Main Thing " is you have to Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare ".
_______________________________
If your not able to follow these 4 things no illicit s.ex, no g.ambling, no d.rugs, no meat-eating then don,t worry but chanting of this holy name ( Hare Krishna Maha-Mantra ) is very-very and very important.
Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare " and be happy.
if you still don,t believe on me then chant any other name for 5 Min's and chant this holy name for 5 Min's and you will see effect. i promise you it works And chanting at least 16 rounds ( each round of 108 beads ) of the Hare Krishna maha-mantra daily.
____________
Here is no Question of Holy Books quotes, Personal Experiences, Faith or Belief. i accept that Sometimes Faith is also Blind. Here is already Practical explanation which already proved that every`1 else in this world is nothing more then Busy Foolish and totally idiot.
_________________________
Source(s):
every `1 is already Blind in this world and if you will follow another Blind then you both will fall in hole. so try to follow that person who have Spiritual Eyes who can Guide you on Actual Right Path. ( my Authority & Guide is my Spiritual Master " Srila Prabhupada " )
_____________
if you want to see Actual Purpose of human life then see this link : ( triple w ( d . o . t ) asitis ( d . o . t ) c . o . m {Bookmark it })
read it complete. ( i promise only readers of this book that they { he/she } will get every single answer which they want to know about why im in this material world, who im, what will happen after this life, what is best thing which will make Human Life Perfect, and what is perfection of Human Life. ) purpose of human life is not to live like animal cuz every`1 at present time doing 4 thing which are sleeping, eating, s.ex & fear. purpose of human life is to become freed from Birth after birth, Old Age, Disease, and Death.

HomeWork Help Please Respond ASAP!!!

[CENTER][B]The Sum of three times a number and 18 is -39. Find the number.[/B][/CENTER]
I was always confused with these problems and never understood them. Any help would be much appreciated!!
Thank you!

HomeWork Help Please Respond ASAP!!!

The phrase a number means an arbitrary variable, let's call it x.
Three times a number:
3x
And 18 means we add 18
3x + 18
The word is means equal to, so we set 3x + 18 equal to -39
3x + 18 = -39
This is your algebraic expression. If you want to solve for x, plug it into the [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']search engine[/URL] and you get x = -19

How many times bigger is 3^9 than 3^3

How many times bigger is 3^9 than 3^3
Using exponent rules, we see that:
3^9 = 3^3 * 3^6
So our answer is [B]3^6 times bigger[/B]

How old am I if 400 reduced by 2 times my age is 244?

How old am I if 400 reduced by 2 times my age is 244?
Let my age be a. We're given:
400 - 2a = 244
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D244&pl=Solve']type this equation into our search engine [/URL]and we get:
a = [B]78[/B]

How old am I if 400 reduced by 3 times my age is 124?

How old am I if 400 reduced by 3 times my age is 124?
Let my age be a. We're given an algebraic expression:
[LIST]
[*]3 times my age means we multiply a by 3: 3a
[*]400 reduced by 3 times my age means we subtract 3a from 400:
[*]400 - 3a
[*]The word [I]is[/I] mean an equation, so we set 400 - 3a equal to 124
[/LIST]
400 - 3a = 124
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D124&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]92[/B]

How old am I if: 210 reduced by 3 times my current age is 4 times my current age?

How old am I if: 210 reduced by 3 times my current age is 4 times my current age?
Let your current age be a. We're given:
[LIST]
[*]210 reduced by 3 times current age = 210 - 3a
[*]4 times current age = 4a
[*]The word [I]is[/I] means equal to. So we set 210 - 3a equal to 4a
[/LIST]
210 - 3a = 4a
To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=210-3a%3D4a&pl=Solve']type this equation into our search engine [/URL]and we get:
a = [B]30[/B]

How old am I of 400 reduced by 2 times my age is 224

How old am I of 400 reduced by 2 times my age is 224
[LIST=1]
[*]Let my age be a.
[*]2 times my age: 2a
[*]400 reduced by 2 times my age: 400 - 2a
[*]The phrase [I]is [/I]means an equation. So we set 400 - 2a equal to 224 for our algebraic expression
[/LIST]
[B]400 - 2a = 224
[/B]
If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D224&pl=Solve']type this equation into our search engine[/URL] and we get:
a = [B]88[/B]

I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13

I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13 and subtract 13.What is my number?
Take a number (n):
The first operation is multiply 5 times n, and then add 39:
5n + 139
The second operation is multiply 13 times n and subtract 13:
13n - 13
Set both operations equal to each other since they result in [I]the same number[/I]
5n + 139 = 13n - 13
[URL='https://www.mathcelebrity.com/1unk.php?num=5n%2B139%3D13n-13&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]n = 19[/B]

If 11 times a number is added to twice the number, the result is 104

If 11 times a number is added to twice the number, the result is 104
Let [I]the number[/I] be an arbitrary variable we call x.
11 times a number:
11x
Twice the number (means we multiply x by 2):
2x
The phrase [I]is added to[/I] means we add 2x to 11x:
11x + 2x
Simplify by grouping like terms:
(11 + 2)x = 13x
The phrase [I]the result is[/I] means an equation, so we set 13x equal to 104:
13x = 104 <-- This is our algebraic expression
To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=13x%3D104&pl=Solve']we type it in our search engine[/URL] and we get:
x = [B]8[/B]

If 12 times a number is added to twice the number, the result is 112

If 12 times a number is added to twice the number, the result is 112.
Let the number be n, so we have:
12n + 2n = 112
Combine like terms
14n = 112
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=14n%3D112&pl=Solve']equation solver[/URL], we get [B]n = 8[/B].

If 2 times an integer x is increased by 5

If 2 times an integer x is increased by 5
2 times an integer x:
2x
The phrase [I]increased by[/I] means we add, so we add 5 to 2x:
[B]2x + 5[/B]

If 200 bacteria triple every 1/2 hour, how much bacteria in 3 hours

If 200 bacteria triple every 1/2 hour, how much bacteria in 3 hours
Set up the exponential function B(t) where t is the number of tripling times:
B(d) = 200 * (3^t)
3 hours = 6 (1/2 hour) periods, so we have 6 tripling times. We want to know B(6):
B(6) = 200 * (3^6)
B(6) = 200 * 729
B(6) = [B]145,800[/B]

If 3 times a number added to 2 is divided by the number plus 4 the result is 4/3

If 3 times a number added to 2 is divided by the number plus 4 the result is 4/3
Take this in pieces, where "a number" means an arbitrary variable, let's call it "x".
[LIST=1]
[*]3 times a number --> 3x
[*]3 times a number added to 2 --> 3x + 2
[*]The number plus 4 --> x + 4
[*]is divided by --> (3x + 2)/(x + 4)
[*]the result is 4/3 --> (3x + 2)/(x + 4) = 4/3
[/LIST]

If 4 times a number is added to 9, the result is 49

If 4 times a number is added to 9, the result is 49.
[I]A number[/I] means an arbitrary variable, let's call it x.
4 [I]times a number[/I] means we multiply x by 4
4x
[I]Added to[/I] 9 means we add 9 to 4x
4x + 9
[I]The result is[/I] means we have an equation, so we set 4x + 9 equal to 49
[B]4x + 9 = 49[/B] <-- This is our algebraic expression
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%2B9%3D49&pl=Solve']we type it in the search engine[/URL] and get x = 10

If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integ

If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integer.
[LIST]
[*]Let the integer be "x".
[*]Square the integer: x^2
[*]7 times the square: 7x^2
[*]5 times the integer: 5x
[*]Add them together: 7x^2 + 5x
[*][I]The result is[/I] means an equation, so we set 7x^2 + 5x equal to 2
[/LIST]
7x^2 + 5x = 2
[U]This is a quadratic equation. To get it into standard form, we subtract 2 from each side:[/U]
7x^2 + 5x - 2 = 2 - 2
7x^2 + 5x - 2 = 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=7x%5E2%2B5x-2%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get two solutions:
[LIST=1]
[*]x = 2/7
[*]x= -1
[/LIST]
The problem asks for an integer, so our answer is x[B] = -1[/B].
[U]Let's check our work by plugging x = -1 into the quadratic:[/U]
7x^2 + 5x - 2 = 0
7(-1)^2 + 5(-1) - 2 ? 0
7(1) - 5 - 2 ? 0
0 = 0
So we verified our answer, [B]x = -1[/B].

If 72 is added to a number it will be 4 times as large as it was originally

If 72 is added to a number it will be 4 times as large as it was originally
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
72 added to a number:
x + 72
4 times as large as it was originally means we take the original number x and multiply it by 4:
4x
Now, the phrase [I]it will be[/I] means an equation, so we set x + 72 equal to 4x to get our final algebraic expression:
[B]x + 72 = 4x[/B]
[B][/B]
If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B72%3D4x&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]24[/B]

if 9 times a number is decreased by 6, the result is 111

if 9 times a number is decreased by 6, the result is 111
A number means an arbitrary variable, let's call it x.
9 times a number:
9x
Decreased by 6
9x - 6
The result is 11, this means we set 9x - 6 equal to 11
[B]9x - 6 = 11
[/B]
To solve this equation for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=9x-6%3D11&pl=Solve']equation calculator[/URL]

If Distance equals Speed times Time (D = S x T), then what does time equal in terms of speed and dis

If Distance equals Speed times Time (D = S x T), then what does time equal in terms of speed and distance?
Divide each side by S to isolate T:
D/S = S x T/S
Cancel the S's on the right side:
[B]T = D/S[/B]

if flip a coin 4 times, what is the probability of getting all 4 tails

if flip a coin 4 times, what is the probability of getting all 4 tails.
P(Tails) = 1/2
Each flip is independent, so we have:
[URL='https://www.mathcelebrity.com/cointoss.php?hts=TTTT&hct=+2&tct=+1&fct=+5>=no+more+than&nmnl=+2&htpick=tails&calc=1&montect=500&pl=Calculate+Probability']P(TTTT)[/URL] = [B]1/16[/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 p=2x is even, then p^2 is also even

if p=2x is even, then p^2 is also even
p^2 = 2 * 2 * x^2
p^2 = 4x^2
This is [B]true [/B]because:
[LIST]
[*]If x is even, then x^2 is even since two evens multiplied by each other is even and 4x^2 is even
[*]If x is odd, the x^2 is odd, but 4 times the odd number is always even since even times odd is even
[/LIST]

If Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how ma

If Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how many of each coin does he have?
Using q for quarters and n for nickels, and using 525 cents as $5.25, we're given two equations:
[LIST=1]
[*]q = 4n
[*]0.25q + 0.05n = 5.25
[/LIST]
Substitute equation (1) into equation (2) for q:
0.25(4n) + 0.05n = 5.25
Multiply through and simplify:
n + 0.05n = 5.25
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B0.05n%3D5.25&pl=Solve']type it in our search engine[/URL] and we get:
n = [B]5
[/B]
To get q, we plug in n = 5 into equation (1) above:
q = 4(5)
q = [B]20[/B]

If the number of professors in a college is P and the number is students S, and there are 14 times a

If the number of professors in a college is P and the number is students S, and there are 14 times as many students as professors
14 times as many means we multiply:
[B]S = 14P[/B]

If there are 10^30 grains of sand on Beach A, how many grains of sand are there on a beach the has 1

If there are 10^30 grains of sand on Beach A, how many grains of sand are there on a beach the has 10 times the sand as Beach A? (Express your answer using exponents.)
10^30 * 10 = 10^(30 + 1) = [B]10^31[/B]

If you buy a computer directly from the manufacturer for $3,509 and agree to repay it in 36 equal in

If you buy a computer directly from the manufacturer for $3,509 and agree to repay it in 36 equal installments at 1.73% interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
[U]Determine the monthly payment[/U]
The monthly payment is [B]$114.87[/B] using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=3059&av=&pmt=&n=36&i=1.73&check1=1&pl=Calculate']annuity calculator[/URL]
[U]Determine the total payments made[/U]
Total payment is 36 times $114.87 = $4,135.37
[U]Now determine the total interest paid[/U]
Take the total payments of $4,135.37 and subtract the original loan of $3,059 to get interest paid of [B]$1,076.37[/B]

If you throw a die for two times, what is the probability that you will get a one on the first throw

If you throw a die for two times, what is the probability that you will get a one on the first throw or a one on the second throw (or both)?
[LIST]
[*]P(1) on first roll and P(anything on second roll) = 1/6 * 1 = 1/6
[*]P(anything on first roll) and P(1) on second roll = 1 * 1/6 = 1/6
[*]Add those together: 1/6 + 1/6 = 2/6 = [B]1/3[/B]
[/LIST]

If you toss a fair coin 6 times, what is the probability of getting all tails?

If you toss a fair coin 6 times, what is the probability of getting all tails?
We [URL='https://www.mathcelebrity.com/cointoss.php?hts=TTTTTT&hct=+2&tct=+1&fct=+5>=no+more+than&nmnl=+2&htpick=tails&calc=1&montect=500&pl=Calculate+Probability']type in our search engine [I]TTTTTT [/I]and we get[/URL]:
P(TTTTTT) = [B]1/64 or 0.015625[/B]

In 1 year, a baseball player got 195 hits in 600 times. What is his batting average?

In 1 year, a baseball player got 195 hits in 600 times. What is his batting average?
Batting Average = Hits / Times at Bat
Batting Average = 195 / 600
[URL='https://www.mathcelebrity.com/perc.php?num=196&den=600&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Batting Average[/URL] = [B]0.327[/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 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 right now be b.
We have, in 16 years, Ben's age will be 3 times what his age is now:
b + 16 = 3b
Subtract b from each side:
2b = 16
Divide each side by 2
[B]b = 8[/B]
Check our work:
16 years from now, Ben's age is 8 + 16 = 24
And, 8 x 3 = 24

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 45 years, Gabriela will be 4 times as old as she is right now.

In 45 years, Gabriela will be 4 times as old as she is right now.
Let a be Gabriela's age. we have:
a + 45 = 4a
Subtract a from each side:
3a = 45
Divide each side by a
[B]a = 15[/B]

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 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 the year 1989, Luke's age was 3 times Rachel's age and Rachel's age was 3 times Dan's age. If Dan

In the year 1989, Luke's age was 3 times Rachel's age and Rachel's age was 3 times Dan's age. If Dan's age was n, how old were Rachel and Luke?
Rachel's age = 3 * Dan's age
Rachel's age = 3n
Luke's age = 3 times Rachel's age
Luke's age = 3(3n)
Luke's age = [B]9n[/B]

Is it correct to word "10% * 50 + 50" as "10% upper 50"?

I read that as 10% times 50 plus 50

Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only

[SIZE=4]Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only 5 times as old as William?
[U]Express Ishaan and William's age since today where y is the number of years since today, we have:[/U]
i = 72+y
w = 4+y
[U]We want the time for Ishaan age will be 5 times William's age:[/U]
i = 5w
72 + y = 5(4 + y)
We [URL='https://www.mathcelebrity.com/1unk.php?num=72%2By%3D5%284%2By%29&pl=Solve']plug this equation into our search engine [/URL]and get:
y = [B]13[/B]
[/SIZE]

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]

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

Jenny makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.
Since Jenny makes 9 dollars for each hour of work, then her total pay (p) is her hourly rate times the number of hours worked:
[B]p = 9h[/B]

Jerry rolls a dice 300 times what is the estimated numbers the dice rolls on 6

Jerry rolls a dice 300 times what is the estimated numbers the dice rolls on 6
Expected Value = Rolls * Probability
Since a 6 has a probability of 1/6, we have:
Expected Value = 300 * 1/6
Expected Value = [B]50[/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]

Joan bought 3 cars for $9876 how much did Joan pay?

3 cars times $9,876 for each car = $29,628

Joanie multiplied 0.78 times 0.34 and got the product 26.52. What error did she make

Joanie multiplied 0.78 times 0.34 and got the product 26.52. What error did she make
[B]She didn't move the decimal point over 2 spots[/B]:
0.78 * 0.34 = 0.2652

Juliana answered 42 times correctly on an 80-item quiz, while her sister Angela answered 21 items co

Juliana answered 42 times correctly on an 80-item quiz, while her sister Angela answered 21 items correctly on a 40-item quiz. Do they have the same portion of correct answers?
Let's compare based on correct answers to questions:
Juliana = 42/80 = 0.525
Angela = 21/40 = 0.525
So yes, they do have the same portion of correct answers.
But there's another way to solve this:
[LIST=1]
[*]Divide Juliana's the top and bottom of Juliana's fraction by 2.
[*]We picked 2 as a GCF shown in our calculator.
[*]Type [URL='https://www.mathcelebrity.com/gcflcm.php?num1=42&num2=80&num3=&pl=GCF']GCF of 42 and 80[/URL].
[/LIST]
Divide top and bottom of Juliana's fraction by the GCF of 2
42/2 = 80/2 = 21/40
This ratio equals Angela's.

Julio had a coin box that consisted of only quarters and dimes. The number of quarters was three tim

Julio had a coin box that consisted of only quarters and dimes. The number of quarters was three times the number of dimes. If the number of dimes is n, what is the value of coins in the coin box?
Set up monetary value:
[LIST]
[*]Value of the dimes = 0.1n
[*]Value of the quarters = 0.25 * 3n = 0.75n
[/LIST]
Add them together
[B]0.85n[/B]

Karin has 3 to spend in the arcade. The game she likes costs 50c per play. What are the possible num

Karin has 3 to spend in the arcade. The game she likes costs 50c per play. What are the possible numbers of times that she can play?
[U]Let x = the number of games Karin can play with her money[/U]
0.5x = 3
[U]Divide each side by 0.5[/U]
[B]x = 6[/B]

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

Kevin is 4 times old as Daniel and is also 6 years older than Daniel

Kevin is 4 times old as Daniel and is also 6 years older than Daniel.
Let k be Kevin's age and d be Daniel's age. We have 2 equations:
[LIST=1]
[*]k = 4d
[*]k = d + 6
[/LIST]
Plug (1) into (2):
4d = d + 6
Subtract d from each side:
4d - d = d - d + 6
Cancel the d terms on the right side and simplify:
3d = 6
Divide each side by 3:
3d/3 = 6/3
Cancel the 3 on the left side:
d = 2
Plug this back into equation (1):
k = 4(2)
k = 8
So Daniel is 2 years old and Kevin is 8 years old

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]

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]

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 times the difference of 2p and 4r

m times the difference of 2p and 4r
The difference of 2p and 4r:
2p - 4r
m times the difference:
[B]m(2p - 4r)[/B]

m times the sum of n and 5

Sum of n and 5
n + 5
m times that sum
m(n + 5)

Marco takes 2 quizzes each week. Write an equation that shows the relationship between the number of

Marco takes 2 quizzes each week. Write an equation that shows the relationship between the number of weeks x and the total number of quizzes y. Write your answer as an equation with y first, followed by an equals sign.
Our total quizzes equal 2 times the number of weeks (x):
[B]y = 2x[/B]

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than 11. What is the youngest age Warren can be?
Let m be Marty's age and w be Warren's age. We have two equations:
(1) m = 6w - 3
(2) m + w > 11
Plug (1) into (2)
6w - 3 + w > 11
Combine w terms
7w - 3 > 11
Add 3 to each side
7w > 14
Divide each side by 7
w > 2 which means [B]w = 3[/B] as the youngest age.

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

Mike received a penny on December 1st. On December 2nd he received 2 cents. December 3rd another 4 c

Mike received a penny on December 1st. On December 2nd he received 2 cents. December 3rd another 4 cents and December 4th he received 8 cents. If his money continues to double, how much will he earn on December 25th?
We have 24 doubling times starting December 2 to December 25
0.01 * 2^24
0.01 * 16,777,216
[B]167,772.16[/B]

Milan plans to watch 2 movies each month. Write an equation to represent the total number of movies

Milan plans to watch 2 movies each month. Write an equation to represent the total number of movies n that he will watch in m months.
Number of movies equals movies per month times the number of months. So we have:
[B]n = 2m[/B]

Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opp

Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent's serves. Assume her opponent serves 8 times. Show all work. Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution.
a) What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?
b) Find the probability that that she returns at least 1 of the 8 serves from her opponent.
(c) How many serves can she expect to return?
a) [B]n = 8
p = 0.2[/B]
q = 1 - p
q = 1 - 0.2
[B]q = 0.8
[/B]
b) [B]0.4967[/B] on our [URL='http://www.mathcelebrity.com/binomial.php?n=+8&p=0.2&k=1&t=+5&pl=P%28X+>+k%29']binomial calculator[/URL]
c) np = 8(0.2) = 1.6 ~ [B]2[/B] using the link above

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.

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.

n increased by the difference between 10 times n and 9

n increased by the difference between 10 times n and 9
Take this algebraic expression in pieces:
[LIST]
[*]10 times n: 10n
[*]The difference between 10 times n and 9: 10n - 9
[*]n increased by the difference...: [B]n + (10n - 9)[/B]
[/LIST]

n is equal to 135 less than the quantity 61 times n

n is equal to 135 less than the quantity 61 times n
61 times n:
61n
135 less than the quantity 61 times n
61n - 135
We set n equal to this expression:
[B]n = 61n - 135[/B]

n times 146, reduced by 94 is the same as h

n times 146, reduced by 94 is the same as h
n time 146
146n
Reduced by 94
146n - 94
Is the same as h means an equation:
[B]146n - 94 = h[/B]

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]

Nervous Speaker #1 says the word "um" 8 times each minute. Nervous Speaker #2 says the word "um" 10

[SIZE=5]Nervous Speaker #1 says the word "um" 8 times each minute. Nervous Speaker #2 says the word "um" 10 times each minute. Working together, how many minutes will it take them to say the word "um" 270 times?
[/SIZE]
[SIZE=4]In one minute, Nervous speaker 1 and 2 say "um" 8 + 10 = 18 times per minute.
We want to know how many minutes it takes for both of them to say 270 "um"s.
We divide 270/18 to get [B]15 minutes[/B][/SIZE]

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 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]

Nine times the sum of a number and 6

Nine times the sum of a number and 6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 6 means we add 6 to x:
x + 6
9 times the sum:
[B]9(x + 6)[/B]

nine times x is twice the sum of x and five

nine times x is twice the sum of x and five
Take this algebraic expression in 4 pieces:
[U]Step 1: nine time x:[/U]
9x
[U]Step 2: The sum of x and five means we add 5 to x:[/U]
x + 5
[U]Step 3: The word [I]twice[/I] means we multiply the sum x + 5 by 2:[/U]
2(x + 5)
[U]Step 4: The word [I]is[/I] means equal to, so we set 9x equal to 2(x + 5) to get our final algebraic expression of:[/U]
[B]9x = 2(x + 5)[/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

output is 3 times the input x

output is 3 times the input x
Let output be y. We have:
[B]y = 3x[/B]

p is equal to r plus 2 times q

p is equal to r plus 2 times q
2 times q:
2q
r plus 2 times q:
r + 2q
is equal to means we set p equal to r + 2q
[B]p = r + 2q[/B]

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

please solve the fourth word problem

The sum of three numbers is
105
. The first number is
5
less than the second. The third number is
3
times the second. What are the numbers?

please solve the third word problem

A Web music store offers two versions of a popular song. The size of the standard version is
2.7
megabytes (MB). The size of the high-quality version is
4.7
MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was
4200
MB. How many downloads of the standard version were there?

please solve the third word problem

A Web music store offers two versions of a popular song. The size of the standard version is
2.7
megabytes (MB). The size of the high-quality version is
4.7
MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was
4200
MB. How many downloads of the standard version were there?
Let s be the standard version downloads and h be the high quality downloads. We have two equations:
[LIST=1]
[*]h = 3s
[*]2.7s + 4.7h = 4200
[/LIST]
Substitute (1) into (2)
2.7s + 4.7(3s) = 4200
2.7s + 14.1s = 4200
Combine like terms:
16.8s = 4200
Divide each side by 16.8
[B]s = 250[/B]

q increased by the difference between 18 times q and 5

q increased by the difference between 18 times q and 5
Take this algebraic expression in parts.
18 times q:
18q
The difference between 18 times q and 5 means we subtract 5 from 18q:
18q - 5
q increased by the difference between 18 times q and 5 means we add 18q - 5 to q:
q + (18q - 5)
[B]q + 18q - 5[/B]
IF we want to simplify, we group like terms:
[B]19q - 5[/B]

q is equal to 207 subtracted from the quantity 4 times q

q is equal to 207 subtracted from the quantity 4 times q
4 time q
4q
207 subtracted from 4 times q:
4q - 207
Set this equal to q:
[B]4q - 207 = q [/B]<-- This is our algebraic expression
To solve for q, [URL='https://www.mathcelebrity.com/1unk.php?num=4q-207%3Dq&pl=Solve']type this equation into the search engine[/URL]. We get:
[B]q = 69[/B]

Robert has 45 dollars. He buys 6 tshirts and has 7 dollars left over. How much did each tshirt cost?

Let x be the price of one t-shirt. Set up an equation:
6 times the number of t-shirts plus 7 dollars left over get him to a total of 45
6x = 45 - 7
6x = 38
Divide each side by 6
[B]x = 6.33[/B]

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

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 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 space for flipping a coin 3 times

sample space for flipping a coin 3 times
Each flip gives us 2 possible outcomes, heads or tails. So we have:
2 * 2 * 2 = 8 possible outcomes
[LIST=1]
[*]HHH
[*]HHT
[*]HTH
[*]HTT
[*]THH
[*]THT
[*]TTH
[*]TTT
[/LIST]

Sergeant U has 360 rounds of ammunition to distribute to Lance Corporal (LCpl) F, Lance Corporal (LC

Sergeant U has 360 rounds of ammunition to distribute to Lance Corporal (LCpl) F, Lance Corporal (LCpl) M and Lance Corporal (LCpl) Z in the ratio 3:5:7. How many rounds did Lance Corporal (LCpl) M receive?
Our ratio denominator is:
3 + 5 + 7 = 15
Lance Corporal (LCpl) M gets 5:15 of the ammunition. [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F15&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we see that 5/15 = 1/3
So we take 360 rounds of ammunition times 1/3:
360/3 = [B]120[/B]

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants i

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants it to be 5 times as long as it is wide. What dimensions should the play area be?
Sheila wants:
[LIST=1]
[*]l =5w
[*]2l + 2w = 100 <-- Perimeter
[/LIST]
Substitute (1) into (2)
2(5w) + 2w = 100
10w + 2w = 100
12w = 100
Divide each side by 12
[B]w = 8.3333[/B]
Which means l = 5(8.3333) -->[B] l = 41.6667[/B]

Six Less than the total of three times a number and negative eight

Six Less than the total of three times a number and negative eight.
Let's take this in pieces:
Three times a number = 3x
The total of this and negative eight means we subtract eight
3x - 8
Six Less than this total means we subtract 6
3x - 8 - 6
Simplify by combining like terms:
[B]3x - 14[/B]

Some scientists believe that there are 10^87 atoms in the entire universe. The number googolplex is

Some scientists believe that there are 10^87 atoms in the entire universe. The number googolplex is a 1 followed by a googol of zeros. If each atom in the universe is used as a zero, how many universes would you need in order to have enough zeros to write out completely the number googolplex?
10^100 zeros in the entire googolplex and 10^87 atoms in the universe
10^100 / 10^87 = [B]10^13 times as many zeros in the googolplex as there are atoms in the universe[/B]

Sonia visited a park in California that had redwood trees. When Sonia asked how tall a certain large

Sonia visited a park in California that had redwood trees. When Sonia asked how tall a certain large redwood tree was, the ranger said that he wouldn't tell its height, but would give Sonia a clue. How tall is the redwood tree Sonia asked about?
Sonia said the tree is 64 times my height. The tree is also 112 feet taller than the tree next to it. The two trees plus my height total 597.5 feet.
[LIST]
[*]Rangers's height = n
[*]Tree height = 64n
[*]Smaller tree height = 64n - 112
[*]Total height = 64n - 112 + 64n = 597.5
[/LIST]
Solve for [I]n[/I] in the equation 64n - 112 + 64n = 597.5
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(64 + 64)n = 128n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
128n - 112 = + 597.5
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants -112 and 597.5. To do that, we add 112 to both sides
128n - 112 + 112 = 597.5 + 112
[SIZE=5][B]Step 4: Cancel 112 on the left side:[/B][/SIZE]
128n = 709.5
[SIZE=5][B]Step 5: Divide each side of the equation by 128[/B][/SIZE]
128n/128 = 709.5/128
n = 5.54296875
Tree height = 64 * ranger height
Tree height = 64 * 5.54296875
Tree height = [B]354.75 feet[/B]

square root of x times the square root of y

square root of x times the square root of y
square root of x:
sqrt(x)
square root of y:
sqrt(y)
square root of x times the square root of y
[B]sqrt(x) * sqrt(y)[/B]

Squaring a number equals 5 times that number

Squaring a number equals 5 times that number.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Squaring this number:
x^2
5 times this number means we multiply by 5:
5x
The phrase [I]equals[/I] means we set both expressions equal to each other:
[B]x^2 = 5x [/B] <-- This is our algebraic expression
If you want to solve for x, then we subtract 5x from each side:
x^2 - 5x = 5x - 5x
Cancel the 5x on the right side, leaving us with 0:
x^2 - 5x = 0
Factor out x:
x(x - 5)
So we get x = 0 or [B]x = 5[/B]

Stacy and Travis are rock climbing. Stacys rope is 4 feet shorter than 3 times the length of Travis

Stacy and Travis are rock climbing. Stacys rope is 4 feet shorter than 3 times the length of Travis rope. Stacys rope is 23 feet long. Write and solve an equation to find the length t of Travis rope.
Let Stacy's rope be s. Travis's rope be t. We have:
s = 3t - 4
s = 23
So [B]3t - 4 = 23
[/B]
[URL='http://www.mathcelebrity.com/1unk.php?num=3t-4%3D23&pl=Solve']Paste this equation into our search engine[/URL] to get [B]t = 9[/B].

Start with x , subtract 6, then times by 3.

Start with x , subtract 6, then times by 3.
We start with x:
x
Subtract 6:
x - 6
The phrase [I]times by[/I] means we multiply (x - 6) by 3
[B]3(x - 6) [/B] <-- This is our algebraic expression
If the problem asks you to multiply through, then you'd have:
3x - 18

Subtract 6 from 7 times s

Subtract 6 from 7 times s
7 times s
7s
Subtract 6 from that
[B]7s - 6[/B]

sum of 5 times h and twice g is equal to 23

sum of 5 times h and twice g is equal to 23
Take this [U]algebraic expressions[/U] problem in pieces.
Step 1: 5 times h:
5h
Step 2: Twice g means we multiply g by 2:
2g
Step 3: sum of 5 times h and twice g means we add 2g to 5h
5h + 2g
Step 4: The phrase [I]is equal to[/I] means an equation, so we set 5h + 2g equal to 23:
[B]5h + 2g = 23[/B]

sum of twice w and 3 times l

sum of twice w and 3 times l
Twice w means we multiply w by 2:
2w
3 times l:
3l
When we see the phrase [I]sum of[/I], we add:
[B]2w + 3l[/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

The 4/7 part of a number is 84 . What is the number?

The 4/7 part of a number is 84 . What is the number?
We multiply 4/7 * 84.
7 goes into 84 12 times, so we have:
4 * 12 = [B]48[/B]

The area of a desert in Africa is 12 times the area of a desert in Asia. If the area of a desert in

The area of a desert in Africa is 12 times the area of a desert in Asia. If the area of a desert in Asia is Y square miles, express the area of a desert in Africa as an algebraic expression in Y.
[B]Africa Area = 12Y[/B]

The cost of a gallon of milk (m) is .50 more than 5 times the cost of a gallon of water (w). If a ga

The cost of a gallon of milk (m) is .50 more than 5 times the cost of a gallon of water (w). If a gallon of milk cost 3.75, what is the cost of a gallon of water?
We're given:
m = 5w + 0.50
m = $3.75
Set them equal to each other:
5w + 0.50 = 3.75
[URL='https://www.mathcelebrity.com/1unk.php?num=5w%2B0.50%3D3.75&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 0.65[/B]

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y
Take this in algebraic expression in parts:
[U]Term 1[/U]
[LIST]
[*]The square of y means we raise y to the 2nd power: y^2
[*]5 times the square of y: 5y^2
[/LIST]
[U]Term 2[/U]
[LIST]
[*]2 times y: 2y
[*]The square of 2 times y: (2y)^2 = 4y^2
[*]7 divide by the square of 2 times y: 7/4y^2
[/LIST]
[U]The difference of these terms is written as Term 1 minus Term 2:[/U]
[LIST]
[*]5y^2/4y^2
[/LIST]
[U]The cube of the difference means we raise the difference to the power of 3:[/U]
[B](5y^2/4y^2)^3[/B]

the cube of the difference of 5 times x and 4

the cube of the difference of 5 times x and 4
Take this algebraic expression in pieces:
5 times x:
5x
The difference of 5x and 4 means we subtract 4 from 5x:
5x - 4
We want to cube this difference, which means we raise the difference to the power of 3.
[B](5x - 4)^3[/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 3 times x and 4

[U]3 times x:[/U]
3x
[U]The difference between 3x and 4 means we subtract:[/U]
3x - 4

the difference between 7 times a number and 9 less than a number

the difference between 7 times a number and 9 less than a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
7 times a number means we multiply x by 7
7x
9 less than a number means we subtract 9 from x
x - 9
The difference between the two expressions means we subtract (x - 9) from 7x
7x - (x - 9)
Simplifying this, we have:
7x - x + 9
Grouping like terms, we get:
[B]6x + 9[/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 a number and 6 is the same as 5 times the sum of the number and 2. What is the num

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?
We have two expressions:
[U]Expression 1: [I]The difference of a number and 6[/I][/U]
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The difference of a number and 6 means we subtract 6 from x:
x - 6
[U]Expression 2: [I]5 times the sum of the number and 2[/I][/U]
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The sum of a number and 2 means we add 2 to x:
x + 2
5 times the sum means we multiply x + 2 by 5
5(x + 2)
[U]For the last step, we evaluate the expression [I]is the same as[/I][/U]
This means equal to, so we set x - 6 equal to 5(x + 2)
[B]x - 6 = 5(x + 2)[/B]

The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown n

The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown number.
The phrase a number uses the variable w.
3 times w is written as 3w
The difference of 3w and 6 is written as 3w - 6
Set this equal to 7
[B]3w - 6 = 7
[/B]
This is our algebraic expression. To solve this equation for w, we [URL='http://www.mathcelebrity.com/1unk.php?num=3w-6%3D7&pl=Solve']type the algebraic expression into our search engine[/URL].

the difference of x and 5 is 2 times of x

the difference of x and 5 is 2 times of x
The difference of x and 5 means we subtract 5 from x
x - 5
The word [I]is[/I] means an equation, so we set x - 5 equal to 2 times x
[B]x - 5 = 2x[/B]

The doctor told Anna that tomorrow she will have to check her blood pressure every 15 minutes from 1

The doctor told Anna that tomorrow she will have to check her blood pressure every 15 minutes from 10:00 AM to 4:00 PM. How many times does she have to take her blood pressure?
10:00 A.M. to 4:00 P.M. is 6 hours.
Each hour is 60 minutes
60 minutes divided by 15 minutes equals 4 blood pressure checks per hour.
4 blood pressure checks per hour * 6 hours = [B]24 blood pressure checks[/B]

The doubling time of a population of flies is 8 hours by what factor does a population increase in 2

The doubling time of a population of flies is 8 hours.
a) By what factor does a population increase in 24 hours?
b) By what factor does the population increase in 2 weeks?
a) If the population doubles every 8 hours, then it doubles 3 times in 24 hours, since 24/8 = 3.
So 2 * 3 = 6. The increase factor is [B]6[/B]
b) Since a) is one full day, we now need to know how much it doubles in 14 days, which is 2 weeks. We take our factor of 6 for each day, and multiply it by 14: 14 * 6 = [B]84[/B]

The larger of 2 numbers is 1 more than 3 times the smaller number

The larger of 2 numbers is 1 more than 3 times the smaller number.
Let the larger number be l. Let the smaller number be s. The algebraic expression is:
3 times the smaller number is written as:
3s
1 more than that means we add 1
3s + 1
Our final algebraic expression uses the word [I]is[/I] meaning an equation. So we set l equal to 3s + 1
[B]l = 3s + 1[/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 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.
Using our [URL='http://www.mathcelebrity.com/rectangle-word-problems.php?t1=perimeter&v1=120&t2=length&v2=6&op=less&v3=3&t4=times&t5=width&pl=Calculate']rectangular word problem calculator[/URL], we have:
[LIST]
[*][B]l = 43.5[/B]
[*][B]w = 16.5[/B]
[/LIST]

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.
Using our [URL='http://www.mathcelebrity.com/rectangle-word-problems.php?t1=perimeter&v1=120&t2=length&v2=6&op=less&v3=3&t4=times&t5=width&pl=Calculate']rectangle word problem calculator[/URL], we get:
[LIST]
[*][B]w = 16.5[/B]
[*][B]l = 43.5[/B]
[/LIST]

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 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 length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length a

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length and width.
A flag is a rectangle shape. So we have the following equations
Since P = 2l + 2w, we have 2l + 2w = 60
l = 7w - 2
Substitute Equation 1 into Equation 2:
2(7w -2) + 2w = 60
14w - 4 + 2w = 60
16w - 4 = 60
Add 4 to each side
16w = 64
Divide each side by 16 to isolate w
w = 4
Which means l = 7(4) - 2 = 28 - 2 = 26

The negative of the sum of C and D is equal to the difference of the negative of C and D

The negative of the sum of C and D is equal to the difference of the negative of C and D
The negative of the sum of C and D means -1 times the sum of C and D
-(C + D)
Distribute the negative sign:
-C - D
the difference of the negative of C and D means we subtract D from negative C
-C - D
So this statement is [B]true[/B] since -C - D = -C - D

The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Fin

The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Find the length and the width of the rectangle.
l = 4w - 15
Perimeter = 2l + 2w
Substitute, we get:
400 = 2(4w - 15) + 2w
400 = 8w - 30 + 2w
10w - 30 = 400
Add 30 to each side
10w = 370
Divide each side by 10 to isolate w
w = 37
Plug that back into our original equation to find l
l = 4(37) - 15
l = 148 - 15
l = 133
So we have (l, w) = (37, 133)

the product of k and 70, minus 15

the product of k and 70, minus 15
Take this algebraic expression in pieces:
The product of k and 70 means we multiply 70 times k
70k
The word [I]minus[/I] means we subtract 15 from 70k
[B]70k - 15[/B]

the reciprocal of the product a and b

the reciprocal of the product a and b
Take this algebraic expression in pieces:
The product a and b means we multiply a times b
ab
The [I]reciprocal[/I] means we take 1 over ab
[B]1/ab[/B]

The square of a number is always nonnegative.

The square of a number is always nonnegative.
This is true, and here is why:
Suppose you have a positive number n.
n^2 = n * n
A positive times a positive is a positive
Suppose you have a negative number -n
(-n)^2 = -n * -n = n^2
A negative times a negative is a positive.

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 18. 3 times the greater number exceeds 4 times the smaller number by 5. Find

The sum of 2 numbers is 18. 3 times the greater number exceeds 4 times the smaller number by 5. Find the numbers.
Let the first number be x. The second number is y. We have:
[LIST=1]
[*]x + y = 18
[*]3x = 4y + 5
[/LIST]
Rearrange (2), by subtracting 4y from each side:
3x - 4y = 5
So we have a system of equations:
[LIST=1]
[*]x + y = 18
[*]3x - 4y = 5
[/LIST]
Using our [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y+%3D+18&term2=3x+-+4y+%3D+5&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[B]x = 11
y = 7[/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 times a number and -2, added to 4 times a number

the sum of 2 times a number and -2, added to 4 times a number.
The phrase, [I]a number[/I], means an arbitrary variable, let's call it x.
2 times a number
2x
The sum of means add, so we add -2, which is the same as subtracting 2
2x - 2
Now, we add 4 times x
2x - 2 + 4x
Combining like terms, we have:
(2 + 4)x - 2
[B]6x - 2[/B]

the sum of 2 times x and 3 times y diminished by 12

the sum of 2 times x and 3 times y diminished by 12
2 times x:
2x
3 times y:
3y
the sum of 2 times x and 3 times y
2x + 3y
the sum of 2 times x and 3 times y diminished by 12
[B]2x + 3y - 12[/B]

The sum of 2 times x and 5 times y is 7

The sum of 2 times x and 5 times y is 7
2 times x:
2x
5 times y:
5y
The sum of 2 times x and 5 times y:
2x + 5y
The word [I]is[/I] means equal to, so we set 2x + 5y equal to 7:
[B]2x + 5y = 7[/B]

The sum of 3 times the square of a number and negative 7

The sum of 3 times the square of a number and negative 7
[U]The phrase [I]a number[/I] means an arbitrary variable, let's call it x:[/U]
x
[U]The square of a number means we raise x to the power of 2:[/U]
x^2
[U]3 times the square of a number:[/U]
3x^2
[U]The sum of 3 times the square of a number and negative 7[/U]
[B]3x^2 - 7[/B]

the sum of 5 times p and 10

the sum of 5 times p and 10
5 times p
5p
and 10 means add 10
[B]5p + 10[/B]

the sum of 6 and 7, plus 5 times a number, is -12

the sum of 6 and 7, plus 5 times a number, is -12
The sum of 6 and 7 means we add the two numbers:
6 + 7
This evaluates to 13
Next, we take 5 times a number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So we multiply x by 5:
5x
The first two words say [I]the sum[/I], so we add 13 and 5x
13 + 5x
The word [I]is[/I] means an equation, so we set 13 + 5x equal to -12
[B]13 + 5x = -12[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=13%2B5x%3D-12&pl=Solve']type this algebraic expression into our search engine[/URL] and you get:
[B]x = -5[/B]

The sum of 6 times a number and -8, added to 3 times a number

The sum of 6 times a number and -8, added to 3 times a number
The phrase "a number", means an arbitrary variable, let's call it x.
6 times a number:
6x
And means we add, so we have
6x - 8
Added to 3 times a number
6x - 8 + 3x
Combine like terms:
[B]9x - 8[/B]

the sum of 7 times y and 3 is equal to 2

the sum of 7 times y and 3 is equal to 2
7 times y:
7y
The sum of 7 times y and 3 means we add 3 to 7y
7y + 3
The phrase [I]is equal to[/I] means an equation, so we set 7y + 3 equal to 2
[B]7y + 3 = 2[/B]

The sum of a number and 34 times the number

The sum of a number and 34 times the number
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
34 times the number:
34x
The sum of a number and 34 times the number means we add both terms together:
x + 34x

the sum of a number times 3 and 30 is less than 17

the sum of a number times 3 and 30 is less than 17
A number is denoted as an arbitrary variable, let's call it x.
x
Times 3 means we multiply x by 3:
3x
The sum of a number times 3 and 30 means we add 30 to 3x above
3x + 30
Is less than 17 means we have an inequality, so we set 3x + 30 less than 17
3x + 30 < 17
To solve for x and see the interval notation, use [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B30%3C17&pl=Solve']our calculator[/URL]:

The sum of six times a number and 1 is equal to five times the number. Find the number.

The sum of six times a number and 1 is equal to five times the number. Find the number.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
6 times a number is written as:
6x
the sum of six times a number and 1 is written as:
6x + 1
Five times the number is written as:
5x
The phrase [I]is equal to[/I] means an equation, so we set 6x + 1 equal to 5x:
6x + 1 = 5x
[URL='https://www.mathcelebrity.com/1unk.php?num=6x%2B1%3D5x&pl=Solve']Plugging this into our search engine[/URL], we get:
x = [B]-1[/B]

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. Ho

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now?
Let Levi's current age be l. Let Renee's current age be r. Were given two equations:
[LIST=1]
[*]l + r = 89
[*]l - 7 = 4(r - 7)
[/LIST]
Simplify equation 2 by multiplying through:
[LIST=1]
[*]l + r = 89
[*]l - 7 = 4r - 28
[/LIST]
Rearrange equation 1 to solve for r and isolate l by subtracting l from each side:
[LIST=1]
[*]r = 89 - l
[*]l - 7 = 4r - 28
[/LIST]
Now substitute equation (1) into equation (2):
l - 7 = 4(89 - l) - 28
l - 7 = 356 - 4l - 28
l - 7 = 328 - 4l
To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l-7%3D328-4l&pl=Solve']type the equation into our search engine[/URL] and we get:
l = [B]67[/B]

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times the unit digit. Find the number.
Let the digits be (x)(y) where t is the tens digit, and o is the ones digit. We're given:
[LIST=1]
[*]x + y = 10
[*]10x+ y = 15y + 4
[/LIST]
Simplifying Equation (2) by subtracting y from each side, we get:
10x = 14y + 4
Rearranging equation (1), we get:
x = 10 - y
Substitute this into simplified equation (2):
10(10 - y) = 14y + 4
100 - 10y = 14y + 4
[URL='https://www.mathcelebrity.com/1unk.php?num=100-10y%3D14y%2B4&pl=Solve']Typing this equation into our search engine[/URL], we get:
y = 4
Plug this into rearranged equation (1), we get:
x = 10 - 4
x = 6
So our number xy is [B]64[/B].
Let's check our work against equation (1):
6 + 4 ? 10
10 = 10
Let's check our work against equation (2):
10(6)+ 4 ? 15(4) + 4
60 + 4 ? 60 + 4
64 = 64

The sum of the square of a number and 7 times a number

The sum of the square of a number and 7 times a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Square the number:
x^2
7 times the number means we multiply x by 7:
7x
The sum means we add x^2 and 7x
[B]x^2 + 7x[/B]

The Sum of three times a number and 18 is -39. Find the number

The Sum of three times a number and 18 is -39. Find the number.
A number means an arbitrary variable, let us call it x.
Three times x:
3x
The sum of this and 18:
3x + 18
Is means equal to, so we set 3x + 18 = -39
3x + 18 = -39
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']equation solver[/URL], we get [B]x = -19[/B]

The sum of twice an integer and 3 times the next consecutive integer is 48

The sum of twice an integer and 3 times the next consecutive integer is 48
Let the first integer be n
This means the next consecutive integer is n + 1
Twice an integer means we multiply n by 2:
2n
3 times the next consecutive integer means we multiply (n + 1) by 3
3(n + 1)
The sum of these is:
2n + 3(n + 1)
The word [I]is[/I] means equal to, so we set 2n + 3(n + 1) equal to 48:
2n + 3(n + 1) = 48
Solve for [I]n[/I] in the equation 2n + 3(n + 1) = 48
We first need to simplify the expression removing parentheses
Simplify 3(n + 1): Distribute the 3 to each term in (n+1)
3 * n = (3 * 1)n = 3n
3 * 1 = (3 * 1) = 3
Our Total expanded term is 3n + 3
Our updated term to work with is 2n + 3n + 3 = 48
We first need to simplify the expression removing parentheses
Our updated term to work with is 2n + 3n + 3 = 48
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(2 + 3)n = 5n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
5n + 3 = + 48
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 3 and 48. To do that, we subtract 3 from both sides
5n + 3 - 3 = 48 - 3
[SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE]
5n = 45
[SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE]
5n/5 = 45/5
Cancel the 5's on the left side and we get:
n = [B]9[/B]

The sum of x and 10 equals the sum of 2 times x and 12

The sum of x and 10 equals the sum of 2 times x and 12
The sum of x and 10 means we add 10 to x:
x + 10
2 times x means we multiply x by 2:
2x
the sum of 2 times x and 12 means we add 12 to 2x:
2x + 12
The sum of x and 10 equals the sum of 2 times x and 12:
x + 10 + (2x + 12)
Distribute the parentheses, and we get:
x + 10 + 2x + 12
Group like terms:
(1 + 2)x + 10 + 12
[B]3x + 22[/B]

The top part of the tree is 3 times as long as the trunk which equation can tulia use to find t the

The top part of the tree is 3 times as long as the trunk which equation can tulia use to find t the length of the trunk
Let p be the top part of the tree.
We have p = 3t.
Divide by 3, we get t = [B]p/3[/B]

the total of 3 times the cube of u and the square of u

the total of 3 times the cube of u and the square of u
[U]The cube of u means we raise u to the power of 3:[/U]
u^3
[U]The square of u means we raise u to the power of 2:[/U]
u^2
The total of both of these is found by adding them together:
[B]u^3 + u^2[/B]

The value of 3 times the quantity of 4 + x is greater than 6 less than x.

The value of 3 times the quantity of 4 + x is greater than 6 less than x.
3 times the quantity 4 + x
3(4 + x)
6 less than x
x - 6
3 times the quantity 4 + x is greater than x - 6
[B]3(4 + x) > x - 6[/B]

The world record for the mile in the year 1865 was held by Richard Webster of England when he comple

The world record for the mile in the year 1865 was held by Richard Webster of England when he completed a mile in 4 minutes and 36.5 seconds. The world record in 1999 was set by Hicham El Guerrouj when he ran a mile in 3 minutes and 43.13 seconds.
If both men ran the mile together, how many feet behind would Richard Webster be when Hichem El Guerrouj crossed the finish line?
Change times to seconds:
[LIST]
[*]4 minutes and 36.5 seconds = 4*60 + 36.5 = 240 + 36.5 = 276.5 seconds
[*]3 minute and 43.13 seconds = 3*60 + 43.13 = 180 + 43.13 = 223.13 seconds
[/LIST]
Now, find the distance Richard Webster travelled in 3 minutes and 43.13 seconds which is when Hiram El Guerrouj crossed the finish line.
1 mile = 5280 feet:
Set up a proportion of distance in feet to seconds where n is the distance Richard Webster travelled
5280/276.5 = n/223.13
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5280&num2=n&den1=276.5&den2=223.13&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
n = 4260.85 feet
Distance difference = 5280 - 4260.85 = [B]1019.15 feet[/B]

There are 10 true or false questions on a test. You do not know the answer to 4 of the questions, so

There are 10 true or false questions on a test. You do not know the answer to 4 of the questions, so you guess. What is the probability that you will get all 4 answers right?
Probability you guess right is 1/2 or 0.5.
Since each event is independent of the other events, we multiply 1/2 4 times:
1/2 * 1/2 * 1/2 * 1/2 = [B]1/16[/B]

There are 15 houses in a neighborhood. Nine of the houses have 6 people in them. The remaining house

There are 15 houses in a neighborhood. Nine of the houses have 6 people in them. The remaining houses have 4 people in them. How many people are in a neighborhood.
9 houses * 6 people per house = 54 people
The remaining houses equal 15 total houses - 9 houses = 6 houses
6 houses remaining times 4 people in each house = 24 people
54 people + 24 people = [B]78 people in the neighborhood[/B]

There are 480 calories per hour. An officer swims 1.5 hours for 30 days. How many calories is that?

There are 480 calories per hour. An officer swims 1.5 hours for 30 days. How many calories is that?
1.5 hours per day times 30 days = 45 total hours.
480 calories per hour times 45 total hours = [B]21,600 total calories[/B].

There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The

There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The difference between 2 times the first number and 3 times the second number is 24. Find the two numbers.
Let the first number be x and the second number be y. We have 2 equations:
[LIST=1]
[*]4x + 3y = 24
[*]2x - 3y = 24
[/LIST]
Without doing anything else, we can add the 2 equations together to eliminate the y term:
(4x + 2x) + (3y - 3y) = (24 + 24)
6x = 48
Divide each side by 6:
[B]x = 8
[/B]
Substitute this into equation (1)
4(8) + 3y = 24
32 + 3y = 24
[URL='https://www.mathcelebrity.com/1unk.php?num=32%2B3y%3D24&pl=Solve']Type 32 + 3y = 24 into our search engine[/URL] and we get [B]y = 2.6667[/B].

Three tennis balls each have a radius of 2 inches. They are put into a 12 inch high cylinder with a

Three tennis balls each have a radius of 2 inches. They are put into a 12 inch high cylinder with a 4 inch diameter. What is the volume of the space remaining in the cylinder?
Volume of each ball is 4/3 ?r^3
V = 4/3 * 3.1415 * 2^3
V = 1.33 * 3.1415 * 8 = 33.41 cubic inches
The volume of 3 balls is:
V = 3(33.41)
V = 100.23
Volume of the cylinder is area of circle times height:
V = 3.14 * 2 * 2 * 1 = 150.72
Volume of remaining space is:
V = Volume of cylinder - Volume of 3 balls
V = 150.72 - 100.23
V = [B]50.49[/B]

Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli departm

Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli department at least 260 person-hours per week. Tom has one part-time employeewho works 20 hours per week. Each full-time employee works 40 hours per week. Write an inequality to determine n, the number of full-time employees Tom must schedule, so that his employees will work at least 260 person-hours per week.
Set up the inequality:
[LIST]
[*]Add the part-timer's hours of 20
[*]Full time hours is 40 times n employees
[*]At least means greater than or equal to, so we use the >= sign
[/LIST]
[B]40n + 20 >= 260[/B]

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

twice the difference between x and 28 is 3 times a number

twice the difference between x and 28 is 3 times a number
The difference between x and 28:
x - 28
Twice the difference means we multiply x - 28 by 2:
2(x - 28)
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
3 times a number:
3x
The word [I]is[/I] means equal to, so we set 2(x - 28) equal to 3x:
[B]2(x - 28) = 3x[/B]

twice the difference of a number and 3 is equal to 3 times the sum of a number and 2

twice the difference of a number and 3 is equal to 3 times the sum of a number and 2.
We've got 2 algebraic expressions here. Let's take them in parts.
Left side algebraic expression: twice the difference of a number and 3
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]The word [I]difference[/I] means we subtract 3 from the variable x
[*]x - 3
[*]Twice this difference means we multiply (x - 3) by 2
[*]2(x - 3)
[/LIST]
Right side algebraic expression: 3 times the sum of a number and 2
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]The word [I]sum[/I] means we add 2 to the variable x
[*]x + 2
[*]3 times the sum means we multiply (x + 2) by 3
[*]3(x + 2)
[/LIST]
Now, we have both algebraic expressions, the problem says [I]is equal to[/I]
This means we have an equation, where we set the left side algebraic expression equal to the right side algebraic expression using the equal sign (=) to get our answer
[B]2(x - 3) = 3(x + 2)[/B]

twice the difference of a number and 55 is equal to 3 times the sum of a number and 8

twice the difference of a number and 55 is equal to 3 times the sum of a number and 8
Take this algebraic expression in pieces.
Left side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The difference of this number and 55 means we subtract 55 from x
x - 55
Twice the difference means we multiply x - 55 by 2
2(x - 55)
Right side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 8 means we add 8 to x
x + 8
3 times the sum means we multiply x + 8 by 3
3(x + 8)
Now that we have the left and right side of the expressions, we see the phrase [I]is equal to[/I]. This means an equation, so we set the left side equal to the right side:
[B]2(x - 55) = 3(x + 8)[/B]

Two coins are flipped 2 times. Calculate the total outcomes of these coins.

Two coins are flipped 2 times. Calculate the total outcomes of these coins.
2 coins * 2 outcomes per coin = 4 possible outcomes
[LIST=1]
[*][B]H,H[/B]
[*][B]H,T[/B]
[*][B]T,H[/B]
[*][B]T,T[/B]
[/LIST]

What is the probability of rolling 12, 5 times in a row?

The only way you can roll a 12 with two dice is 6 and 6. Since each die roll is independent, we have:
[LIST]
[*]P(12) = P(6) * P(6)
[*]P(12) = 1/6 * 1/6
[*]P(12) = 1/36.
[/LIST]
Now, what is the probability we roll a 12 five times in a row? The same rules apply, each new roll is independent of the last, so we multiply:
[LIST]
[*]P(12, 12, 12, 12, 12) = 1/36 * 1/36 * 1/36 * 1/36 * /36
[*]P(12, 12, 12, 12, 12) = [B]1/60,466,176[/B] or [B]1.65381717e-8[/B]
[/LIST]

What pair of consecutive integers gives the following: 7 times the smaller is less than 6 times the

What pair of consecutive integers gives the following: 7 times the smaller is less than 6 times the larger?
Let x and y be consecutive integers, where y = x + 1
We have 7x < 6y as our inequality.
Substituting x, y = x + 1, we have:
7x < 6(x + 1)
7x < 6x + 6
Subtracting x from each side, we have:
x < 6, so y = 6 + 1 = 7
(x, y) = (6, 7)

When 20 is subtracted from 3 times a certain number, the result is 43

A certain number means an arbitrary variable, let's call it x
x
3 times x
3x
20 is subtracted from 3 time x
3x - 20
The result is means equal to, so we set 3x - 20 equal to 43 for our algebraic expression
[B]3x - 20 = 43
[/B]
If you need to solve this, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-20%3D43&pl=Solve']equation calculator[/URL]:
[B]x = 21[/B]

When 28 is subtracted from the square of a number, the result is 3 times the number. Find the negati

When 28 is subtracted from the square of a number, the result is 3 times the number. Find the negative solution.
Let the number be n.
Square of a number:
n^2
28 is subtracted from the square of a number:
n^2 - 28
3 times the number:
3n
[I]The result is[/I] mean an equation, so we set n^2 - 28 = 3n
n^2 - 28 = 3n
Subtract 3n from each side:
n^2 - 3n - 28 = 3n - 3n
The right side cancels to 0, so we have:
n^2 - 3n - 28 = 0
This is a quadratic equation in standard form, so we [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-3n-28%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']use our quadratic calculator[/URL] to solve:
We get two solutions for n:
n = (-4, 7)
The question asks for the negative solution, so our answer is:
[B]n = -4[/B]

When 3 consecutive positive integers are multiplied, the product is 16 times the sum of the 3 intege

When 3 consecutive positive integers are multiplied, the product is 16 times the sum of the 3 integers. What is the difference of the product minus the sum?
Let the 3 consecutive positive integers be:
[LIST=1]
[*]x
[*]x + 1
[*]x + 2
[/LIST]
The product is:
x(x + 1)(x + 2)
The sum is:
x + x + 1 + x + 2 = 3x + 3
We're told the product is equivalent to:
x(x + 1)(x + 2) = 16(3x + 3)
x(x + 1)(x + 2) = 16 * 3(x + 1)
Divide each side by (x + 1)
x(x + 2) = 48
x^2 + 2x = 48
x^2 + 2x - 48 = 0
Now subtract the sum from the product:
x^2 + 2x - 48 - (3x + 3)
[B]x^2 - x - 51[/B]

When 39 is added to a number, the result is 40 times the number. Find the number. Let n be the unkn

When 39 is added to a number, the result is 40 times the number. Find the number. Let n be the unknown number. Write the translated equation below.
[LIST=1]
[*]39 added to a number is written as n + 39
[*]40 times the number is written as 40n
[*]The result is means we have an equation, so set (1) equal to (2)
[/LIST]
n+ 39 = 40n
Running [URL='http://www.mathcelebrity.com/1unk.php?num=n%2B39%3D40n&pl=Solve']n + 39 = 40n through the search engine[/URL], we get[B] n = 1[/B].

When 4 is subtracted from the square of a number, the result is 3 times the number. Find the positiv

When 4 is subtracted from the square of a number, the result is 3 times the number. Find the positive solution.
Let the number be n. We have:
n^2 - 4 = 3n
Subtract 3n from each side:
n^2 - 3n - 4 = 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-3n-4%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Typing this quadratic equation into the search engine[/URL], we get:
n = (-1, 4)
The problem asks for the positive solution, so we get [B]n = 4[/B].

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the num

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. Find the number
The phrase [I]a number, [/I]means an arbitrary variable, let's call it "x".
4 times a number, increased by 40, means we multiply 4 times x, and then add 40
4x + 40
100 decreased by the number means we subtract x from 100
100 - x
The problem tells us both of these expressions are the same, so we set them equal to each other:
4x + 40 = 100 - x
Add x to each side:
4x + x + 40 = 100 - x + x
The x's cancel on the right side, so we have:
5x + 40 = 100
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B40%3D100&pl=Solve']Typing this equation into the search engine[/URL], we get [B]x = 12[/B].

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the num

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
4 times a number means we multiply x by 4:
4x
Increased by 40 means we add 40 to 4x:
4x + 40
100 decreased by the number means we subtract x from 100:
100 - x
The phrase [I]is the same as[/I] means equal to, so we set 4x + 40 equal to 100 - x
4x + 40 = 100 - x
Solve for [I]x[/I] in the equation 4x + 40 = 100 - x
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 4x and -x. To do that, we add x to both sides
4x + 40 + x = -x + 100 + x
[SIZE=5][B]Step 2: Cancel -x on the right side:[/B][/SIZE]
5x + 40 = 100
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 40 and 100. To do that, we subtract 40 from both sides
5x + 40 - 40 = 100 - 40
[SIZE=5][B]Step 4: Cancel 40 on the left side:[/B][/SIZE]
5x = 60
[SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE]
5x/5 = 60/5
x = [B]12[/B]
Check our work for x = 12:
4(12) + 40 ? 100 - 12
48 + 40 ? 100 - 12
88 = 88

When 54 is subtracted from the square of a number, the result is 3 times the number.

When 54 is subtracted from the square of a number, the result is 3 times the number.
This is an algebraic expression. Let's take it in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it "x".
x
Square the number, means raise it to the 2nd power:
x^2
Subtract 54:
x^2 - 54
The phrase [I]the result[/I] means an equation, so we set x^2 - 54 equal to 3
[B]x^2 - 54 = 3[/B]

When 9 is subtracted from 5 times a number ,the result is 31

When 9 is subtracted from 5 times a number ,the result is 31
A number means an arbitrary variable, let's call it x.
5 times this number is written as 5x.
9 subtracted from this is written as 5x - 9
[I]The result[/I] means we have an equation, so we set [B]5x - 9 = 31[/B]. This is our algebraic expression.
Now if we want to solve for x, we [URL='http://www.mathcelebrity.com/1unk.php?num=5x-9%3D31&pl=Solve']plug this equation into the search engine [/URL]and get [B]x = 8[/B].

Winnie earns an annual salary of $55,117. If she pays $3,715 a year in taxes and receives a paycheck

Winnie earns an annual salary of $55,117. If she pays $3,715 a year in taxes and receives a paycheck every other week, how much does Winnie receive from each paycheck?
Subtract the taxes to get Winnie's Total net pay:
Total Net Pay = Annual Salary - Annual Taxes
Total Net Pay =$55,117 - $3,715
Total Net Pay = $51,402
Now, if Winnie gets paid every other week, and there are 52 weeks in a year, then she gets paid 26 times.
Calculate single paycheck amount
Single Paycheck Amount = Total Net Pay / 26 payments
Single Paycheck Amount = $51,402 / 26
Single Paycheck Amount = [B]$1,977[/B]

Word Problem Help

A man is three times as old as his son was at the time when the father was twice as old as his son will ne two years from now. Find the present ages of each person.

write an algebraic expression for 197 times y

write an algebraic expression for 197 times y
[B]197y
[/B]
This can also be found by typing 197 times y into our search engine

Write p times p times p times p times p times p and n index form

Write p times p times p times p times p times p and n index form
We have p times itself 6 times, so the index form is:
[B]p^6[/B]

Write the verbal expression for: 9x

Write the verbal expression for: 9x
Using our [URL='http://www.mathcelebrity.com/verbalphrase.php?num=9x&pl=Verbal+Phrase']verbal expression calculator[/URL], we get either of the following:
[LIST]
[*][B]9 times x[/B]
[*][B]9 multiplied by x[/B]
[/LIST]

Write these times as 24 hours times: 1:00 pm 8:10 am 4:45 pm 10:12 pm Write these times as 12 hours

Write these times as 24 hours times:
1:00 pm
8:10 am
4:45 pm
10:12 pm
Write these times as 12 hours time:
15:45
7:12
20:38
12:01
Write these times as 24 hours times (any time on or after 1:00 pm, we add 1 to the 12 noon marker:
1:00 pm = 12 + 1 = 13:00
8:10 am = 8:10 <-- since not past 12 noon
4:45 pm = 4 hours and 45 minutes past 12 noon, so we have 16:45
10:12 pm = 10 hours and 12 minutes past 12 noon, so we have 22:12
Write these times as 12 hours time:
15:45 = 15:45 - 12 = 3:45 PM
7:12 = 7:12, not past noon, so 7;12 am
20:38 = 20:38 - 12 = 8:38 PM
12:01 = 12:01 pm

X plus 9 is equal to 3 times x minus 4

X plus 9 is equal to 3 times x minus 4
x plus 9:
x + 9
3 times x minus 4:
3x - 4
The phrase [I]is equal to[/I] means an equation, so we set x + 9 equal to 3x - 4:
[B]x + 9 = 3x - 4[/B]

x plus y times x minus y

x plus y times x minus y
Plus means we add. Minus means we subtract. So we have:
[B](x + y)(x - y)[/B]

x squared times the difference of x and y

x squared times the difference of x and y
x squared means we raise x to the power of 2:
x^2
The difference of x and y
x - y
x squared times the difference of x and y
[B]x^2(x - y)[/B]

You have saved $50 over the last two weeks and decide to treat yourself by buying some new clothes.

You have saved $50 over the last two weeks and decide to treat yourself by buying some new clothes. You go to the store and find two shirts and three pairs of jeans you like. The two shirts are buy-one-get-one half off, at $22.35 each. The three pairs of jeans are buy-two-get-one-free, at $23.70.
Tax Rate for Harmonized Sales Tax is 13%
a. What would be the total for the two shirts (don’t forget to include taxes)?
b. What would be the total for the three pairs of jeans (don’t forget to include taxes)?
c. Which would you buy and why?
a. Half of 22.35 is 11.18
So two shirts cost:
22.35 + 11.18 = 33.53
Cost with Tax of 13% is:
33.53 * 1.13 = [B]37.89
[/B]
b. Three pairs of jeans are calculated by cost of 1 pair times 2 jeans and you get the third one free:
23.70 * 2 = 47.40
Cost with Tax of 13% is:
47.40 * 1.13 = [B]53.56
[/B]
c. Calculate unit cost, which is cost per item
Unit cost of Shirts = 37.89 / 2 = [B]18.95[/B]
Unit cost of Jeans = 53.56 / 3 = [B]17.85
Buy the jeans since they have a lower unit cost[/B]

You put $5500 in a bond fund which has an annual yield of 4.8%. How much interest will be earned in

You put $5500 in a bond fund which has an annual yield of 4.8%. How much interest will be earned in 23 years?
Build the accumulation of principal. We multiply 5,500 times 1.048 raised to the 23rd power.
Future Value = 5,500 (1.048)^23
Future Value =5,500(2.93974392046)
Future Value = 16,168.59
The question asks for interest earned, so we find this below:
Interest Earned = Future Value - Principal
Interest Earned = 16,168.59 - 5,500
Interest Earned = [B]10,668.59[/B]

Your job pays you $7 per hour. What is the algebraic expression if you worked h hours?

Your job pays you $7 per hour. What is the algebraic expression if you worked h hours?
If your pay is rate times hours, we have:
[B]7h[/B]

z , subtract 5 then times by 3

z , subtract 5 then times by 3
Take this algebraic expression two parts:
[LIST]
[*]z subtract 5: z - 5
[*][I]Then times by 3[/I] means we multiply the expression z - 5 by 3
[/LIST]
[B]3(z - 5)[/B]