Maths Olympiad Prep

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Algebra Difficulty 3.9 AMC 10/12 Find the answer South Africa

The number of different positive integers such that nn+4<49\frac{n}{n+4} < \frac{4}{9} is

Pick one

Solution

Multiplying gives us 9n<4n+169n < 4n + 16, i.e. 5n<165n < 16, so n=1n = 1 or 22 or 33.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.