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

2 Answers
Nov 28, 2016

Answer:

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

Answer:

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