Problem: A tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. At the start of a weekend, her win ratio is exactly $0.500$. During the weekend, she plays four matches, winning three and losing one. At the end of the weekend, her win ratio is greater than $.503$. What's the largest number of matches she could've won before the weekend began? Answer: Unpacking, we get that $\frac{w_i}{m} = \frac{1}{2}$ and $\frac{w_i+3}{m+4} > \frac{503}{1000}$. Substituting $m$ in the inequality for $2w_i$, we find $w_i < \frac{988}{6}$. We see that $3 \nmid 988$ so the maximal $w_i$ is given by $w_i = \lfloor \frac{988}{6} \rfloor = 164.$