The sum of three consecutive numbers is 42. What is the smallest of these numbers?

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Answer 1 · 2016-12-16T14:45:31

The smallest of the three consecutive integers summing to 42 is 13.

Let's call the smallest of the three consecutive numbers #s#.

The next two consecutive integers, by definition of consecutive and the fact they are integers as: #s + 1# and #s + 2#

We know there sum is 42 so we can add our three numbers and solve for #s#:

#s + (s + 1) + (s + 2) = 42#

#s + s + 1 + s + 2 = 42#

#3s + 3 = 42#

#3s + 3 - 3 = 42 - 3#

#3s + 0 = 39#

#3s = 39#

#(3s)/3 = 39/3#

#s = 13#

Checking the solution:

The three consecutive integers would be:

#13#

#13 + 1 = 14#

#13 + 2 = 15#

Adding the three integers gives:

#13 + 14 + 15 = 27 + 15 = 42#