06/19/2020 (2011: Countdown Round, Problem 7)

Q: The difference between two numbers is 80% of the sum of the two numbers. What is the sum of the two numbers if the smaller number is 17?

A: 170

Let's say the two numbers are a and b. We set up the equations:

a - b = .8(a + b) and b = 17

That means:

a - 17 = .8(a + 17)

Which, when you open up is:

a - 17 = .8a + 13.6

You isolate the variable:

.2a = 30.6

You divide both sides by .2:

a = 153

a + b = 153 + 17 = 170