Problem of the month. Thinking problem?

Question

Cherise scored 85 on her last math exam of 100 questions. Her teacher has an unusual way of scoring this test. He calculated her score by subtracting 2 times the number of wrong answers from the number of correct answers. If Cherise answered all 100 questions, how many did she get correct?

Answer 1

score = correct - 2*(wrong)

85 = c-2w

but we have c+w=100 so, c=100-w and therefore;

85=100-w-2w

-15=-3w

w=5

Cherise answered 5 questions with the wrong answer.

Answer 2

Hint: if she got $x$ correct, what was her score?

Answer 3

$x =$ # of wrong answers, $y =$ # of correct answers $\implies y - 2x = 85$, and $x + y = 100$. So $$y - 2(100 - y) = 85 \implies 3y = 285 \implies y = 285/3 = 95$$

Answer 4

Let the number of correct answers be $x$. Then the number of incorrect answers is $100 - x$. Thus,

$$x - 2(100 - x) = 85$$

Manipulate and solve directly for $x$, i.e. the number of correct answers.