A child has a piggy bank that contains only quarters and dimes. Altogether, there are 27 coins in the bank and the total value of the coins is $4.50. How many quarters and how many dimes are in the piggy bank?
a. Write a system of linear equations based on the description. Use x to represent the number of quarters and y to represent the number of dimes.
b. Solve the system using the elimination method. Show all the steps leading to your answer.
c. Write 1-2 sentences to explain what the solution means for this situation.