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

1 Answer
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, #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#