Question

Three consecutive multiples of 3 have a sum of 36. What is the greatest number?

Answer 1

The greatest of the three numbers is 15.

The other two numbers are 9 and 12.

Explanation:

The three consecutive multiples of 3 can be written as;

`x`, `x + 3` and `x + 6` with `x + 6` being the greatest.

We know from the problem the sum of these three numbers equal 36 so we can write and solve for `x` through the following:

`x + x + 3 + x + 6 = 36`

`3x + 9 = 36`

`3x + 9 - 9 = 36 - 9`

`3x = 27`

`(3x)/3 = 27/3`

`x = 9`

Because we are looking for the largest we must add `6` to `x` to obtain the largest number:

`6 + 19 = 15`

Answer 2

15

Explanation:

A multiple of 3 can be written `3n` where `n` is a positive integer.
So 3 consecutive multiples of 3 can be written `3n, 3n+3, 3n+6`
The sum of these is 36
`3n+3n+3+3n+6=36`
`9n+9=36`
Divide through by 9
`n+1=4`
`n=3`
If `n=3` then `3n=9` and the three consecutive multiples of three are 9, 12 and 15 which do indeed total 36