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

Let $a$ be the number of problems she answers correctly and $b$ be the number she answered incorrectly. Because she answers all of the questions $a+b=10$ . Her score is equal to $5a-2b=29$ . Use substitution.

$\begin{align*} b&=10-a\\ 5a-2(10-a)&=29\\ 5a-20+2a&=29\\ 7a&=49\\ a&=\boxed{\text{(C)}\ 7} \end{align*}$

2002 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 16	Followed by Problem 18
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2002 AMC 8 Problems/Problem 17

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