Question

There are three consecutive even integers. If twice the first integer added to the third is 268,258, what are all three integer?

Answer 1

89418 , 89420 , 89422

Explanation:

Let `n` be any positive integer. Then `2n` is a even integer (multiplying by 2 makes the number even, because 2 will be a factor of that number and all even numbers are divisible by 2).

`2n + 2` is the next integer and `2n + 4` the next.

(Adding 2 to an even number gives you the next even number, adding 2 again the next even number and so on)

So we have three consecutive integer:

`2n , (2n + 2) ,(2n + 4)`

Twice the first added to the third is `268,258`

`2(2n) + (2n + 4) = 268258`

Solving for `n`:

`4n + 2n + 4 = 268258`

`6n = 268254`

`n = color(blue)(44709)`

So we have:

`2(color(blue)(44709)) , (2(color(blue)(44709)) + 2) , (2(color(blue)(44709)) + 4) ->`

89418##

89420

89422