Question

The sum of two numbers is 48, their difference is 24. What are the numbers?

Answer 1

The two numbers are 12 and 36

Explanation:

First, let's name the two numbers `n` and `m`.

Then we can write:

`n + m = 48`

and

`n - m = 24`

Step 1) Solve the first equation for `n`:

`n + m = 48`

`n + m - color(red)(m) = 48 - color(red)(m)`

`n + 0 = 48 - m`

`n = 48 - m`

Step 2) Substitute `48 - m` for `n` in the second equation and solve for `m`:

`n - m = 24` becomes:

`48 - m - m = 24`

`48 - 2m = 24`

`-color(red)(48) + 48 - 2m = -color(red)(48) + 24`

`0 - 2m = -24`

`-2m = -24`

`(-2m)/color(red)(-2) = (-24)/color(red)(-2)`

`(color(red)(cancel(color(black)(-2)))m)/cancel(color(red)(-2)) = 12`

`m = 12`

Step 3) Substitute `12` for `m` in the solution to the first equation at the end of Step 1 and calculate `n`:

`n = 48 - m` becomes:

`n = 48 - 12`

`n = 36`