Question

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?

Answer 1

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`