You have 59 total coins for a total of $12.05. you only have quarters and dimes. how many of each coin do you have?

Let x = # of quarters let y = # of dimes
0.25x+0.1y=12.05                                       x+y=59
0.25(59-y)+0.1y=12.05                                   x=59-y
14.75-0.25y+0.1y=12.05                                x=59-18
-0.15y=12.05-14.75                                        x=41
-0.15y=-2.7
y=18

therefore, you have 18 dimes and 41 quarters