2014 AIME I Problems/Problem 2

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An urn contains $4$ green balls and $6$ blue balls. A second urn contains $16$ green bals and $N$ blue balls. A single ball is drawn at random from each urn. The probability that both balls are of the same color is $0.58$. Find $N$.

Solution 1:The probability of drawing balls of the same color is the sum of the probabilities of drawing two green balls and of drawing two blue balls. This give us $\frac{29}{50} = \frac{2}{5} \cdot \frac{16}{16+N} + \frac{3}{5} \cdot \frac{N}{16 + N}$

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