Veronica has been saving dimes and quarters. She has 94 coins in all, and the total value is $19.30. How many times and how many quarters does she have?

Veronica has 28 dimes and 66 quarters. I did this problem with the process of elimination. I knew there were 94 coins total, so I plugged in different amounts of dimes and quarters that's sum equaled 94 coins until I got the right answer of $19.30. For example, I tried d (30) + q (64) = 19.3 where d equals 0.1 and q equals 0.25. For this example, the total was 19, 3.00 in dimes and 16 in quarters. Since the price was lower than 19.30, I knew that more of the coins needed to be quarters, since they are worth more. I repeated this process until the math added up correctly.