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AMC 12 Mock Exam 5 Problem 1

Problem 1 of 25

At a school supply store, 33 pencils cost the same as 22 erasers. Mina buys 55 pencils and 44 erasers and pays a total of $5.50\$5.50. How much does one eraser cost?

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Solution

Let an eraser cost ee dollars. A pencil costs 2e3\frac{2e}{3}, so 5⋅2e3+4e=22e3=5.505\cdot\frac{2e}{3}+4e=\frac{22e}{3}=5.50, giving e=3⋅5.522=0.75e=\frac{3\cdot5.5}{22}=0.75. One eraser costs $0.75\boxed{\$0.75}.

Tagged: linear equations in context