# 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 = 20#

#y = 16#

#### Explanation:

Let the two numbers be

We are given:

#(x+y)/2 = 18#

#2x+5y = 120#

Multiply both sides of the first equation by

#x + y = 36#

Subtract

#x = 36 - y#

Substitute this expression for

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

Subtract

#3y = 120 - 72 = 48#

Divide both sides by

#y = 16#

Then substitute that into

#x = 36 - 16 = 20#