Question

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.

Answer 1

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 = 15
Then inputting this into equation A)
A) X + Y = 27
A) X + 15 = 27
X= 12