Question

The sum of two consecutive even integers is 118. How do you find the integers?

Answer 1

`58 + 60 = 118`

Explanation:

Even integers are always separated by 2. So if we have one even number, we can find the next by adding (or subtracting) two.

So, if `x` is even, `x+2` is the next even number and `x-2` is the previous even number.

But how can we be sure that `x` is even?

Any number multiplied by 2 is definitely even, so it is better to call the first even number, `2x`.

Let the first even integer be `2x`
The next even integer will be `2x +2`

Their sum is `118`

`2x + 2x + 2 = 118`
`4x = 116`

`2x = 58 " we did not need to solve for "x`

The consecutive even integers are `58 and 60`

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We could also have just divided by 2 and then added 1 and subtracted 1.

`118 div 2= 59`

`59 - 1 = 58 and 59 + 1 = 60`