Maths Olympiad Prep

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Algebra Difficulty 1.3 Junior Find the answer Canada

If xx% of 60 is 12, then 15% of xx is

Pick one

Solution

Solution 1

Since x%x\% of 60 is 12, then x10060=12\dfrac{x}{100}\cdot 60 = 12 or x=1210060=20x = \dfrac{12\cdot 100}{60} = 20.

Therefore, 15%15\% of xx is 15% of 20, or 0.1520=30.15 \cdot 20 = 3.

Solution 2

Since x%x\% of 60 is 12, then x10060=12\dfrac{x}{100}\cdot 60 = 12 or 60x100=12\dfrac{60x}{100} = 12.

In terms of xx, 15% of xx equals 15100x\dfrac{15}{100}x or 15x100\dfrac{15x}{100}.

Since 60x100=12\dfrac{60x}{100} = 12, then 15x100=14(60x100)=1412=3\dfrac{15x}{100} = \dfrac{1}{4}\left(\dfrac{60x}{100}\right) = \dfrac{1}{4}\cdot 12 = 3.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.