Difference between revisions of "2002 AMC 8 Problems/Problem 17"
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<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== | + | ==Solution 1== |
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. | 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. | ||
| Line 13: | Line 13: | ||
7a&=49\\ | 7a&=49\\ | ||
a&=\boxed{\text{(C)}\ 7} | a&=\boxed{\text{(C)}\ 7} | ||
| + | \end{align*}</cmath> | ||
| + | |||
| + | ==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 <math>x</math> be the number of questions she answers correctly. Then, we will represent the number incorrect by <math>10-x</math>. | ||
| + | |||
| + | <cmath>\begin{align*} | ||
| + | 50-7(10-x)&=29\\ | ||
| + | 50-70+7x&=29\\ | ||
| + | 7x&=49\\ | ||
| + | x&=\boxed{\text{(C)}\ 7} | ||
\end{align*}</cmath> | \end{align*}</cmath> | ||
Revision as of 14:23, 28 July 2013
Contents
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 1
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.
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 
be the number of questions she answers correctly. Then, we will represent the number incorrect by 
.
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
