# 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?

##### 3 Answers

The numbers are:

#### Explanation:

First write an expression for each of the three numbers,

We know the relationship between them so we can use one variable. Choose

Let the first number be

The second number is

The third number is

Their sum is

The numbers are:

Check:

#### Explanation:

1st number =

2nd number =

3rd number =

Checking!

The numbers are

#### Explanation:

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

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

or

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

Substitute equation [3] into equation [1]:

Combine like terms:

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

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

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

Check:

This checks