There are 84 questions on a college entrance examination.

Question

There are 84 questions on a college entrance examination. One point is awarded for each correct answer, and one third of a point is deducted for each incorrect answer. How many questions does Tami need to answer correctly in order to score at least 64 points on the test? Assume that she answers every question.

Answer 1

If we let x = the number of incorrect answers, then (84 - x) = the number of correct answers

 

(84 - x) - (1/3)x ≥ 64

 

Multiply both sides of the inequality by 3 to clear the fraction

 

3(84 - x) - x ≥ 192

 

252 - 3x - x ≥ 192

 

252 - 4x ≥ 192

 

60 - 4x ≥ 0

 

60 ≥ 4x

 

15 ≥ x

 

What does this tell us? Tami can get no more than 15 incorrect and still earn at least a 64 on the test. If there are 84 total questions, that means Tami must get at least 84 - 15 = 69 questions correct on the exam.