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

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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