Question

What are two consecutive even integers such that their sum is equal difference of three times the larger and two times the smaller?

Answer 1

`4 and 6`

Explanation:

Let `x=` the smaller of the consecutive even integers. That means the larger of the two consecutive even integers is`x+2` (because even numbers are 2 values apart).

The sum of these two numbers is `x+x+2.`

The difference of three times the larger number and two times the smaller is `3(x+2)-2(x)`.

Setting the two expressions equal to each other:
`x+x+2=3(x+2)-2(x)`

Simplify and solve:
`2x+2=3x+6-2x`
`2x+2=x+6`
`x=4`

So the smaller integer is `4` and the larger is `6.`