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> | ||
| + | |||
| + | ==Solution== | ||
| + | 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. | ||
| + | |||
| + | <cmath>\begin{align*} | ||
| + | b&=10-a\\ | ||
| + | 5a-2(10-a)&=29\\ | ||
| + | 5a-20+2a&=29\\ | ||
| + | 7a&=49\\ | ||
| + | a&=\boxed{\text{(C)}\ 7} | ||
| + | \end{align*}</cmath> | ||
| + | |||
| + | ==See Also== | ||
| + | {{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?
Solution
Let 
be the number of problems she answers correctly and 
be the number she answered incorrectly. Because she answers all of the questions 
. Her score is equal to 
. Use substitution.
See Also
| 2002 AMC 8 (Problems • Answer Key • Resources) | ||
| 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 | ||
