2017 AMC 8 Problems/Problem 14

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

To solve this problem, first substitute the amount of problems as 100. This means that 50 of the problems were solved alone. 80% of 50 is 40. This means that 48 of the problems were solved together. 90% of 50 is 45. This means that 45+48, so (C) percent of Zoe’s problems were correct.

~pegasuswa

Page

Toolbox

Search

2017 AMC 8 Problems/Problem 14

Problem 14

Solution