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

2 Answers
Nov 28, 2016

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

Nov 28, 2016

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