Answer:
sum = 65
Step-by-step explanation:
You want the sum of the set of 5 consecutive positive integers such that the sum of the even integers in the set is 26.
The sum of even integers will be a multiple of 3 if the middle integer of the set is even. Here, that sum is 26, not a multiple of 3. Hence the middle integer of the set is 26/2 = 13, and the sum of the set is 13·5 = 65.
The sum of the five integers is 65.
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Additional comment
When working "consecutive integer" problems, it is often useful to think in terms of the average of the integers, the middle one of an odd-length set, or the number halfway between the two middle ones of an even-length set.
A set of 5 integers will have either 3 odds and 2 evens, or 3 evens and 2 odds. The set here obviously does not have 3 even integers (whose sum would be 3 times the middle one).
The set is s = {11, 12, 13, 14, 15}. 10 is not in the set, but 11 is. The sum of evens is 12+14=26.