06/04/2020 (2011: National Sprint Round, Problem 8)

Q: On his science test, Jason got 60% of the questions correct. He got 40 of the 60 multiple choice questions correct and 2/5 of the true-false questions correct. If Jason's science test consisted of only multiple choice and true-false questions, how many total questions were on the test?

A: 80

We set up an equation, with x being how many questions were on the true-false section of the test:

.60 = (40 + .4x) ÷ (60 + x)

We multiply both sides by 60 + x and we get:

36 + .6x = 40 + .4x

We isolate the variable and we get:

.6x - .4x = 40 - 36

We simplify the equation and we get:

.2x = 4

We divide both sides by .2 and we get:

x = 20

Because there were both multiple choice AND true-false questions, we add 20 to the number of questions in the multiple choice section, 60, and we get 20 + 60 = 80 questions.