Question

An exam has 30 questions. The professor subtracts 8 points for each incorrect answer and adds 7 for each correct answer. If a student ends up receiving 0 points, how many questions were answered correctly?

Answer 1

Wrong answer = x

Correct answer = y

Total questions: x+y = 30

Rewrite for x: x = 30-y

Total points:

-8x + 7y = 0

replace x with 30-y

-8(30-y) + 7y = 0

Simplify:

-240 + 8y + 7y = 0

Combine like terms:

-240 + 15y = 0

Add 240 to each side:

15y = 240

Divide both sides by 15:

y = 240 / 15

y = 16

There were 16 correct answers

30-16 = 14 wrong answers.