Difference between revisions of "2017 AMC 8 Problems/Problem 14"
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| + | ==Problem 14== | ||
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| + | 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 <math>80\%</math> of the problems she solved alone, but overall <math>88\%</math> of her answers were correct. Zoe had correct answers to <math>90\%</math> of the problems she solved alone. What was Zoe's overall percentage of correct answers? | ||
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| + | <math>\textbf{(A) }89\qquad\textbf{(B) }92\qquad\textbf{(C) }93\qquad\textbf{(D) }96\qquad\textbf{(E) }98</math> | ||
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| + | ==Solution= | ||
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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. | 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 | ~pegasuswa | ||
Revision as of 16:24, 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
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
