The sum of three consecutive integers is 111. What are the integers?

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Answer 1 · 2017-03-13T18:45:47

See the entire solution process below:

First, let's call the first integer: #i#

Because they are consecutive integers the other two integers are:

#i + 1# and #i + 2#

Their sum is #111# so we can write:

#i + i + 1 + i + 2 = 111#

We can now solve as follows:

#i + i + i + 1 + 2 = 111#

#3i + 3 = 111#

#3i + 3 - color(red)(3) = 111 - color(red)(3)#

#3i + 0 = 108#

#3i = 108#

#(3i)/color(red)(3) = 108/color(red)(3)#

#(color(red)(cancel(color(black)(3)))i)/cancel(color(red)(3)) = 36#

#i = 36#

Therefore:

#i + 1 =37# and #i + 2 = 28#

The three consecutive integers whose sum is 111 are:

#36, 37, 38#