The sum of three consecutive integers is 75, what are the integers?

2 Answers
Jun 3, 2015

Three consecutive integers can be written as # (x) , (x+1) , (x+2)#

Adding them:
# (x) + (x+1) + (x+2) = 75#
# 3x +3 = 75#
# 3x = 75 - 3 = 72#
# color(purple)(x = 72/ 3 = 24#

so ,# x+1 = 25 , x+ 2 = 26#

the numbers are #color(purple)(24,25,26#

Jun 7, 2017

Answer:

This is the type of puzzle that we should try to perform as mental math (in your head). The answer is #24, 25, 26.#

Explanation:

To arrive at this answer, we can avoid a lot of math formulas, and the use of a calculator by investigating the given statement and quantities.

Three consecutive integers means three numbers that follow each other like #1,2,3.# So if we add these up we get #6# as a sum.

But in this case the desired sum of three consecutive integers is #75#.
That means we can start by dividing the target sum #75# by #3#.

#75/3= 25to# you have probably memorized that one already.

That means #3xx25=75 or 25+25+25=75#

But if we take a #1# from the first #25# and move it to the third #25#, we arrive at:

#24,25,26to# which are three consecutive integers that sum to 75#.

If you can understand this method and are careful in using it you will save a lot of time when these types of puzzles appear.