Three times one number minus another number equals 34. If the sum of the numbers is 22, what are the two numbers?

8 and 14

Step-by-step explanation:

let the 2 numbers be x and y with x > y

We can model the situation using the following 2 equations

x + y = 22 → (1)

3x - y = 34 → (2)

adding the equations term by term will eliminate the term in y

(x + 3x) + (y - y) = (22 + 34)

4x = 56 (divide both sides by 4)

x = 14

substitute x = 14 into (1)

14 + y = 22 ⇒ y = 22 - 14 = 8