One number is 5 more than another. the difference between their squares is 95. what are the numbers?

Practically you can choose 5 numbers apart and through guess and check get 7 and 12. Mathematically you can use a system of equations: x-y=5 and (x^2)-(y^2) =95. Solve the first one and you get X=y+5 and you can plug that back into the second equation. So ((y+5)^2)-(y^2)=95. Factor it out you get (y^2)+10y+25-(y^2) =95. The y squared cancels out leaving you with 10y+25=95. Subtract 25 from both sides you get 10y=70. Thus y=7. Plug back into the original equation X-7=5 therefore X is 12.

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