What is the greatest of 5 consecutive integers if the sum of these integers equals 185?

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Answer 1 · 2017-02-04T04:19:34

39 is the greatest of the 5 consecutive integers adding to 185.

First, let's define the 5 consecutive integers.

We can call the smallest of the 5 consecutive integers #x#.

Then, by definition of "consecutive integers" the remaining 4 would be:

#x + 1#, #x + 2#, #x + 3# and #x + 4#

The sum of these 5 consecutive integers equals 185 so we can write and solve for #x#:

#x + x + 1 + x + 2 + x + 3 + x + 4 = 185#

#5x + 10 = 185#

#5x + 10 - color(red)(10) = 185 - color(red)(10)#

#5x + 0 = 175#

#5x = 175#

#(5x)/color(red)(5) = 175/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 35#

#x = 35#

We are looking for the greatest of the 5 consecutive integers or #x + 4 -> 35 + 4 = 39#