Answer: 22 dimes, 8 quarters
Explanation: You can guess and check. You know you need more dimes because they are worth less. It would take more dimes to make up 30 coins. And you also know that quarters cannot make .20 exactly. So your number of dimes must make .20. So I guessed numbers that would have .20 left over, and added quarters to get to $4.20.
