You have 50 dimes and 20 quarters. What percent of the value of your money is in quarters?
The amount in quarters is $20\times25$ cents and the total amount is $50\times10+20\times25$ cents. The percent of the value in quarters is $$\frac{20\times25}{50\times10+20\times25}=\frac{500}{500+500}=\frac{500}{1000}=\boxed{50\%}.$$