Question

The sum of three consecutive even numbers is equal to 48. What are the three numbers?

Answer 1

See a solution process below:

Explanation:

First, let's call the smallest number `n`

Then, because they are consecutive even numbers we can add `2` and `4` to `n` to name the other two numbers:

• `n + 2`

• `+ 4`

Now, we can write this equation and solve for `n`:

`n + (n + 2) + (n + 4) = 48`

`n + n + 2 + n + 4 = 48`

`n + n + n +2 + 4 = 48`

`1n + 1n + 1n + 6 = 48`

`(1 + 1 + 1)n + 6 = 48`

`3n + 6 = 48`

`3n + 6 - color(red)(6) = 48 - color(red)(6)`

`3n + 0 = 42`

`3n = 42`

`(3n)/color(red)(3) = 42/color(red)(3)`

`(color(red)(cancel(color(black)(3)))n)/cancel(color(red)(3)) = 14`

`n = 14`

Therefore the other two numbers are:

`n + 2 = 14 + 2 = 16`

`n + 4 = 14 + 4 = 18`

The three numbers are: 14, 16, 18