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.