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

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==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?
 
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?
  
 
<math> \text{(A)}\ 5\qquad\text{(B)}\ 6\qquad\text{(C)}\ 7\qquad\text{(D)}\ 8\qquad\text{(E)}\ 9 </math>
 
<math> \text{(A)}\ 5\qquad\text{(B)}\ 6\qquad\text{(C)}\ 7\qquad\text{(D)}\ 8\qquad\text{(E)}\ 9 </math>
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==Solution==
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Let <math>a</math> be the number of problems she answers correctly and <math>b</math> be the number she answered incorrectly. Because she answers all of the questions <math>a+b=10</math>. Her score is equal to <math>5a-2b=29</math>. Use substitution.
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<cmath>\begin{align*}
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b&=10-a\\
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5a-2(10-a)&=29\\
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5a-20+2a&=29\\
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7a&=49\\
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a&=\boxed{\text{(C)}\ 7}
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\end{align*}</cmath>
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==See Also==
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{{AMC8 box|year=2002|num-b=16|num-a=18}}

Revision as of 20:00, 23 December 2012

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*}

See Also

2002 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 16
Followed by
Problem 18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions