Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.9 Junior Find the answer

If $x$ is $20 \%$ of $y$ and $x$ is $50 \%$ of $z$ , then what percentage is $z$ of $y$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since $x$ is $20 \%$ of $y$ , then $x=\frac{20}{100} y=\frac{1}{5} y$ . Since $x$ is $50 \%$ of $z$ , then $x=\frac{1}{2} z$ . Therefore, $\frac{1}{5} y=\frac{1}{2} z$ which gives $\frac{2}{5} y=z$ . Thus, $z=\frac{40}{100} y$ and so $z$ is $40 \%$ of $y$ .

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