Vanessa S.

asked • 08/21/17# The sum of two consecutive even integers is seventy two

The sum of two consecutive even integers is seventy two

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## 2 Answers By Expert Tutors

Arturo O. answered • 08/21/17

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Experienced Physics Teacher for Physics Tutoring

Assume n is an even number, such that

n + (n + 2) = 72

Then

2n + 2 = 72

2n = 72 - 2 = 70

2n = 70

n = 70/2 = 35, which is not even. Contradiction!

There is no solution. However, as noted by Andrew, the two consecutive odd integers 35 and 37 add up to 72.

Serena N. answered • 08/21/17

Tutor

New to Wyzant
Master's in US History - AP Qualified + Social Sciences and Writing

2n + 1(2n + 2) = 72

2n + 2n + 2 = 72

4n + 2 = 72

- 2 = 72 - 2

4n = 70 35

------ = ----- => n = --- = 17 1/2 or 17.5 (is not an integer)

4 4 2

Arturo O.

It is 2n that needs to be an integer, along with 2n + 2. Both are integers, but both are also odd (2n = 35), so there is no even solution, although 2n and 2n +2 are both integers.

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08/22/17

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Serena N.

08/21/17