Difference between revisions of "2017 AMC 8 Problems/Problem 14"
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Revision as of 18:10, 22 November 2017
Problem 14
Chloe and Zoe are both students in Ms. Demeanor's math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only 
of the problems she solved alone, but overall 
of her answers were correct. Zoe had correct answers to 
of the problems she solved alone. What was Zoe's overall percentage of correct answers?
Solution
Let the number of questions that they solved alone be 
. Let the percentage of problems they correctly solve together be 
%.
As given, ![\[\frac{80x}{100} + \frac{ax}{100} = \frac{2 \cdot 88x}{100}\]](http://latex.artofproblemsolving.com/6/c/2/6c22dec68f64f92c3368913213f608267d1e4a43.png)
.
Hence, 
.
Zoe got 
problems right out of 
. Therefore, Zoe got 
percent of the problems correct.
See Also
| 2017 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 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. 
