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Question 246880: find all sets of three consecutive positive even integers whose sum is less than 40
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
You know the smallest already: 0 is neither positive nor negative, so the first positive integer is 1 and the sum of the three consecutive integers starting with 1 is 1 + 2 + 3 = 6.
Now we need to know the largest set. Let  be the largest of the three integers. Then the next smaller consecutive integer must be  and the one before that is 
And
Since 43 thirds is equal to 14 and one-third, the largest integer less than 43 thirds must be 14.
So, the largest set of three that sum to less than 40 is 12 + 13 + 14 = 39.
Check: 13 + 14 + 15 = 42 > 40, no good.
So, your first set is 1, 2, 3. The second set is 2, 3, 4. And so on until you get to 12, 13, 14. You can fill in the missing sets.
John
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website!
Tutor John thought you said "consecutive positive integers,
not "consecutive positive EVEN integers."
find all sets of three consecutive positive
even integers whose sum is less than 40
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
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