According to the meaning of the question, suppose there are x 50-cent coins, then there are (80-x) 1 yuan coins.

***66 yuan, so the equation can be listed: 0.5x+(80-x)=66.

0.5x-x=66-80

-0.5x=- 14

x= 14/0.5

Solution: x=28

So there are 28 quarters and 52 1 yuan coins.