2020 AMC 8

Complete problem set with solutions and individual problem pages

Problem 15 Medium

Suppose 15\% of x equals 20\% of y. What percentage of x is y?

  • A.

    5

  • B.

    35

  • C.

    75

  • D.

    133 \frac13

  • E.

    300

Answer:C

Solution 1

Since 20\% = \frac{1}{5}, multiplying the given condition by 5 shows that y is 15 \cdot 5 = \boxed{\textbf{(C) }75} percent of x.

 

Solution 2

Letting x=100 (without loss of generality), the condition becomes 0.15\cdot 100 = 0.2\cdot y \Rightarrow 15 = \frac{y}{5} \Rightarrow y=75. Clearly, it follows that y is 75\% of x, so the answer is \boxed{\textbf{(C) }75}.

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