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 `x` and the greater as `y.` Then it is given that

`y=x+5`  ("the greater of two numbers is 5 more than the smaller")

and

`x+2y=22`  ("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 `y` from the first equation into the second and obtain

`x+2(x+5)=22,` or `3x+10=22,` or `3x=12,` `x=4.`

And recall `y=x+5=9.`

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