The average of two numbers is 18. When 2 times the first number is added to 5 times the second number, the result is 120. How do I find the two numbers?

1 Answer
Oct 17, 2015

Express as algebraic equations in two variables x and y then use substitution to find:

x = 20

y = 16

Explanation:

Let the two numbers be x and y.

We are given:

(x+y)/2 = 18

2x+5y = 120

Multiply both sides of the first equation by 2 to get:

x + y = 36

Subtract y from both sides to get:

x = 36 - y

Substitute this expression for x into the second equation to get:

120 = 2x+5y = 2(36 - y) + 5y = 72 - 2y + 5y = 72 + 3y

Subtract 72 from both ends to get:

3y = 120 - 72 = 48

Divide both sides by 3 to get:

y = 16

Then substitute that into x = 36 - y to get:

x = 36 - 16 = 20