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.
Quarters = x Dimes = y A) X + Y = 27 B) .25X + .10Y = 4.50 Multiplying equation B by -4 B) -X -.4 Y = -18 then adding it to A) A) X + Y =27 we get .6 Y = 9 Y = 15Â Then inputting this into equation A) A) X + Y = 27 A) X + 15 = 27 X= 12
