Question

The average of two numbers is 25 and their difference is 8. What are the numbers?

Answer 1

$x;y-the\ numbers\\\\ \left\{\begin{array}{ccc}\frac{x+y}{2}=25&|multiply\ both\ sides\ by\ 2\\x-y=8\end{array}\right\\+\left\{\begin{array}{ccc}x+y=50\\x-y=8\end{array}\right\ \ \ |add\ sides\ of\ the\ equations\\---------\\.\ \ \ \ \ \ \ \ 2x=58\ \ \ \ \ \ \ |divide\ both\ sides\ by\ 2\\.\ \ \ \ \ \ \ \ \ \ x=29\\\\29+y=50\\y=50-29\\y=21\\\\Answer:29\ and\ 21.$