What are 4 consecutive even integers whose sum is 60?

Answer 1

You can solve this using algebra. The hardest part, as usual, is setting up the problem. Here's how I would do it.

First let's choose a representation for the lowest integer. We could just say it equals x, but that wouldn't incorporate our knowledge that it's even. So I think we should represent it as 2x. Then, since consecutive integers are two apart, we can represent the other three by 2x + 2, 2x + 4, and 2x + 6.

Now all we have to do is solve

2x + (2x + 2) + (2x + 4) + (2x + 6) = 60

Combine like terms and we get

8x + 12 = 60

which gives

8x = 48

and finally

x = 6

So the lowest number is 2x = 12, and the rest are 14, 16, and 18.