Question

The sum of three numbers is 52. The first number is `8` less than the second. the third number is `2` times the second. What are the numbers?

Answer 1

The numbers are: `7, 15 and 30`

Explanation:

First write an expression for each of the three numbers,
We know the relationship between them so we can use one variable. Choose `x` as the smallest one.

Let the first number be `x`
The second number is `x+8`
The third number is `2(x+8)`

Their sum is `52`

`x+x+8+2(x+8)=52`

`x+x+8+2x+16=52`

`4x +24 = 52`

`4x = 52-24`

`4x = 28`

`x=7`

The numbers are: `7, 15 and 30`

Check: `7+15+30 = 52`

Answer 2

`7`, `15` and `30`

Explanation:

`(x - 8) + x + 2x = 52`
`4x - 8 = 52`
`4x = 52 + 8`
`4x = 60`
`x = 60/4`
`x = 15`

1st number = `15 - 8 = 7`
2nd number = `15`
3rd number = `15 * 2 = 30`

Checking!
`30 + 15 + 7 = 52`

Answer 3

The numbers are `7, 15, and 30`

Explanation:

"The sum of three numbers is 52" gives you the following equation:

`x+y+z = 52" [1]"`

"the first number is 8 less than the second" gives you the following equation:

`x = y-8`

or

`y = x+8" [2]"`

"the third number is 2 times the second" gives you the following equation:

`z = 2y" [3]"`

Substitute equation [3] into equation [1]:

`x+y+2y = 52`

Combine like terms:

`x+3y = 52" [1.1]"`

Substitute equation [2] into equation equation [1.1]:

`x+3(x+8) = 52`

`4x+24=52`

`4x = 28`

`x = 7`

Use equation [2] to find the value of y:

`y = 7+8`

`y = 15`

Use equation [3] to find the value of z:

`z = 2(15)`

`z = 30`

Check:

`7+15+30=52`

`52 = 52`

This checks