The difference of two numbers is 12 and their mean is 15. Find the two numbers

The difference of two numbers is 12 and their mean is 15. Find the two numbers.

Let the two numbers be x and y. We're given:

1. x - y = 12
2. (x + y)/2 = 15. <-- Mean is an average

Rearrange equation 1 by adding y to each side:
x - y + y = y + 12

Cancelling the y's on the left side, we get:
x = y + 12

Now substitute this into equation 2:
(y + 12 + y)/2 = 15

Cross multiply:
y + 12 + y = 30

Group like terms for y:
2y + 12 = 30

Typing this equation into our search engine, we get:
y = 9

Now substitute this into modified equation 1:
x = y + 12
x = 9 + 12
x = 21