if there are 21 coins that are only quarters and dimes how much can make $4.05 and there has to be 21 coins in total

Let d be number of dimes and q be number of quarters.

 

d + q = 21

 

10d + 25q = 405

 

Multiply the first equation by 10 and subtract from the second equation:

15q = 195.   Hence q = 13

 

Using this in the first equation we have:  

d + 13 = 21.   Hence d = 8

 

13 quarters and 8 dimes.