# Difference between revisions of "2002 AMC 8 Problems/Problem 17"

## Problem

In a mathematics contest with ten problems, a student gains 5 points for a correct answer and loses 2 points for an incorrect answer. If Olivia answered every problem and her score was 29, how many correct answers did she have?

$\text{(A)}\ 5\qquad\text{(B)}\ 6\qquad\text{(C)}\ 7\qquad\text{(D)}\ 8\qquad\text{(E)}\ 9$

## Solution 1

We can simply use the options. If she got five right, her score would be (5*5)-(5*2)=15. That's not right! If she got six right, her score would be (6*5)-(2*4)=22. That's close, but it's still not right! If she got 7 right, her score would be (7*5)-(2*3)=29. Which is what we need! Thus, our answer is \boxed{\text{(C)}\ 7} \end{align*} (Error compiling LaTeX. ! Missing \$ inserted.)

## Solution 2

We can start with the full score, 50, and subtract not only 2 points for each correct answer but also the 5 points we gave her credit for. This expression is equivalent to her score, 29. Let $x$ be the number of questions she answers correctly. Then, we will represent the number incorrect by $10-x$.

\begin{align*} 50-7(10-x)&=29\\ 50-70+7x&=29\\ 7x&=49\\ x&=\boxed{\text{(C)}\ 7} \end{align*}