Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2017 AMC 8 Problems/Problem 14"

(→‎Solution)
(→‎Solution 2)
Line 18: Line 18:
  
 
Assume the total amount of problems is 200, since we are dealing with percentages, and no values. Then, we know that Chloe got 80 problems correct by herself, and that Chloe got 176 problems right in total.  The problems she got right working together, is <math>176-100</math> since she did 100 problems by herself. The problems she got right working together, Zoe also got right.
 
Assume the total amount of problems is 200, since we are dealing with percentages, and no values. Then, we know that Chloe got 80 problems correct by herself, and that Chloe got 176 problems right in total.  The problems she got right working together, is <math>176-100</math> since she did 100 problems by herself. The problems she got right working together, Zoe also got right.
 +
[NOT FINISHED]
  
 
==See Also==
 
==See Also==

Revision as of 02:13, 30 December 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 $80\%$ of the problems she solved alone, but overall $88\%$ of her answers were correct. Zoe had correct answers to $90\%$ of the problems she solved alone. What was Zoe's overall percentage of correct answers?

$\textbf{(A) }89\qquad\textbf{(B) }92\qquad\textbf{(C) }93\qquad\textbf{(D) }96\qquad\textbf{(E) }98$

Solution

Let the number of questions that they solved alone be $x$. Let the percentage of problems they correctly solve together be $a$%. As given, \[\frac{80x}{100} + \frac{ax}{100} = \frac{2 \cdot 88x}{100}\].

Hence, $a = 96$.

Zoe got $\frac{90x}{100} + \frac{ax}{100} = \frac{186x}{100}$ problems right out of $2x$. Therefore, Zoe got $\frac{\frac{186x}{100}}{2x} = \frac{93}{100} = \boxed{\textbf{(C) } 93}$ percent of the problems correct.


Solution 2

Assume the total amount of problems is 200, since we are dealing with percentages, and no values. Then, we know that Chloe got 80 problems correct by herself, and that Chloe got 176 problems right in total. The problems she got right working together, is $176-100$ since she did 100 problems by herself. The problems she got right working together, Zoe also got right. [NOT FINISHED]

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. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2017_AMC_8_Problems/Problem_14&oldid=89276"