The greater of two numbers is 5 more than the smaller. If the smaller is added to twice the greater, the result is 22. Find both of the numbers.

Hello!

Denote the smaller number as and the greater as Then it is given that

 ("the greater of two numbers is 5 more than the smaller")

and

 ("if the smaller is added to twice the greater, the result is 22").

This is the simple system of two linear equations with two variables. Substitute from the first equation into the second and obtain

or or

And recall

So the answer is: the smaller number is 4, the greater is 9.