2014 AIME I Problems/Problem 2

Revision as of 14:25, 14 March 2014 by Niraekjs (talk | contribs) (Solution)

Problem 2

Solution

First, we find the probability both are blue, then the probability both are green, and add the two probabilities which equaling $0.58$. The probability both are blue is $\frac{4}{10}\cdot\frac{16}{16+N}$, and the probability both are green is $\frac{6}{10}\cdot\frac{N}{16+N}$, so \[\frac{4}{10}\cdot\frac{16}{16+N}+\frac{6}{10}\cdot\frac{N}{16+N}=\frac{29}{50}.\] Solving this equation, we get $N=144$.