Question

The sum of three consecutive even integers is 42, what are the integers?

Answer 1

`12`, `14`, and `16`

Explanation:

You know that thee consecutive even integers add up to give `42`.

If you take `2x` to be the first even number of the series, you can say that

`2x + 2 ->` the second number of the series

`(2x + 2) + 2 = 2x + 4 ->` the third number of the series

This means that you have

`overbrace(2x)^(color(blue)("first even no.")) + overbrace((2x + 2))^(color(red)("second even no.")) + overbrace((2x + 4))^(color(purple)("third even no.")) = 42`

This is equivalent to

`6x + 6 = 42`

`6x = 36 implies x = 36/6 = 6`

The three consecutive even integers that add up to `42` are

`2 * x = 12`

`2 * x + 2 = 14`

`2 * x + 4 = 16`