SOLUTION: The sum of two numbers is 12. The difference between the square of the larger number and the square of the smaller number is 48. Find these two numbers.

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Question 708718: The sum of two numbers is 12. The difference between the square of the larger number and the square of the smaller number is 48. Find these two numbers.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
x and y, x%3Cy.

x%2By=12 and y%5E2-x%5E2=48

Using sum equation, x=12-y.
We can make y%5E2-%2812-y%29%5E2=48.
y%5E2-%28144-24y%2By%5E2%29=48
y%5E2-144%2B24y-y%5E2=48
24y-144=48
24y=48%2B144=192
y=192/24

Answer: y=8. This make x=4.