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2024 DMC Mock 10 Problems/Problem 9

Revision as of 21:05, 16 September 2024 by Pateywatey (talk | contribs) (Created page with "If Nathan brings <math>n</math> people with him, then he pays <math>n+1+\frac{100}{n+1}</math> dollars for the gift and the drive. <math>n+1+\frac{100}{n+1}<n+2+\frac{100}{n+2...")
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If Nathan brings $n$ people with him, then he pays $n+1+\frac{100}{n+1}$ dollars for the gift and the drive. $n+1+\frac{100}{n+1}<n+2+\frac{100}{n+2}\rightarrow \frac{100}{n+1}-\frac{100}{n+2}<1\rightarrow\frac{100}{(n+1)(n+2)}>1\rightarrow (n+1)(n+2)>100$. The least $n$ that satisfies this inequality is $n=\boxed{9}$. Alternatively, use guess and check.

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