Question 246880
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Tutor John thought you said "consecutive positive integers,
not "consecutive positive EVEN integers."
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find all sets of three consecutive positive
even integers whose sum is less than 40
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Let n be the smallest. Then the next consecutive positive even
integer is n+2 and the largest is n+4

n + (n+2) + (n+4) < 40
n + n + 2 + n + 4 < 40
3n + 6 < 40
3n < 34
n < 11 1/3

The largest even integer less than 11 1/3 is 10, so the smallest
can be any even integer between 2 and 10.  These are:

1.   2, 4, and 6 are 3 consecutive positive even integers whose sum is 12.
2.   4, 6, and 8 are 3 consecutive positive even integers whose sum is 18.
3.   6, 8, and 10 are 3 consecutive positive even integers whose sum is 24.
4.   8, 10, and 12 are 3 consecutive positive even integers whose sum is 30.
5.   10, 12, and 14 are 3 consecutive positive even integers whose sum is 36.

There are 5 of them.

Edwin</pre>