Question

Two numbers total 36 and have a difference of 12. How do you find the two number?

Answer 1

The two numbers which solve this problem are `12` and `24`

Explanation:

We can write two different equations from the information provided and then use substitution to solve for the two numbers.

First, lets call the numbers we are looking for `m` and `n`.

We now can write:

`m + n = 36` and `m - n = 12`

First, solve the first equation for `m`:

`m + n - n = 36 - n`

`m + 0 = 36 - n`

`m = 36 - n`

Next, we substitute `36 - n` into the second equation for `m` and solve for `n`:

`36 - n - n = 12`

`36 - 2n = 12`

`36 - 2n + 2n - 12 = 12 + 2n - 12`

`36 - 0 - 12 = 0 + 2n`

`24 = 2n`

`24/2 = (2n)/2`

`12 = (cancel(2)n)/cancel(2)`

`12 = n`

Finally, we can substitute `12` for `n` in the solution to the first equation and calculate `m`:

`m = 36 - 12`

`m = 24`