The top three winners in a tennis tournament share the prize money in the ratio 5:3:1.  If the first place winner receives $15,000, what is the total prize money awarded?

 

 

We can set up a proportion:

 

, where s represents the amount the second place winner receives and t the amount the third place finisher receives.

 

Using the first two terms, .  Solving, we get

 

 

Using the first and last terms, .  Solving, we get

 

 

The total is .  So the total awarded is $27,000.