Question

The sum of three consecutive even #s is 144; what are the numbers?

Answer 1

They are 46, 48, 50.

Explanation:

An even number is a multiple of `2`, then can be written as 2n. The next even number after `2n` is `2n+2` and the following is `2n+4.`
So you are asking for which value of `n` it you have

`(2n)+(2n+2)+(2n+4)=144`

I solve it for `n`

`6n+6=144`
`n=138/6=23`.

The three numbers are

`2n=2*23=46`
`2n+2=46+2=48`
`2n+4=46+4=50`

Answer 2

The numbers are 46, 48 and 50.

Explanation:

First define the consecutive even numbers:

Even numbers, such as 8, 10, 12 etc. differ by 2.

We could call the numbers `x, x+2 and x+4`, but there is no guarantee that x is even.

However, an even number can be divided by 2, so any number given as `2x` is definitely even.

SO, let the consecutive even numbers be `2x, 2x + 2 and 2x + 4`
Their sum is 144, so write an equation:

`2x + (2x + 2) + (2x + 4) = 144`

`6x + 6 = 144`
`6x = 138`
`x = 23`

However, we defined the first even number as `2x`.

`2 xx 23 = 46`

The numbers are 46, 48 and 50.