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

Jul 30, 2016

$58 + 60 = 118$

#### 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, $2 x$.

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

Their sum is $118$

$2 x + 2 x + 2 = 118$
$4 x = 116$

$2 x = 58 \text{ we did not need to solve for } x$

The consecutive even integers are $58 \mathmr{and} 60$

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

$118 \div 2 = 59$

$59 - 1 = 58 \mathmr{and} 59 + 1 = 60$