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

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Answer 1 · 2016-07-30T15:36:24

$58 + 60 = 118$ $58 + 60 = 118$

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 $x$ $x$ is even, $x + 2$ $x+2$ is the next even number and $x - 2$ $x-2$ is the previous even number.

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

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

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

Their sum is $118$ $118$

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

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

The consecutive even integers are $58 and 60$ $58 and 60$

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

$118 \div 2 = 59$ $118 div 2= 59$

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