SMOJ wrote:
Let $a,b,c,d$ be positive integers such that $a+c=20$ and $\frac{a}{b}+\frac{c}{d}<1$. Find the maximum possible value of $\frac{a}{b}+\frac{c}{d}$.
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A basketball team's players were successful on $50\%$ of their two-point shots and $40\%$ of their three-point shots, which resulted in 54 points. They attempted $50\%$ more two-point shots than three-point shots. How many three-point shots did they attempt?