Question

Cassie has a total of 110 coins in her piggy bank. All the counts are quarters and dimes. The coins have a total value of 20.30. How many quarters and how many dimes are in the piggy bank

Answer 1

By setting up a system of equations (q + d = 110 and 25q + 10d = 2030), and solving for q and d, we find that Cassie's piggy bank contains 62 quarters and 48 dimes.

Step-by-step explanation:

To determine how many quarters and dimes are in Cassie's piggy bank, we can set up a system of linear equations using the information provided. We can represent the number of quarters as q and the number of dimes as d. The total number of coins is given as 110, which can be expressed as q + d = 110. The total value of all coins is $20.30, or 2030 cents. Since a quarter is worth 25 cents and a dime is worth 10 cents, we can write the value equation as 25q + 10d = 2030.

We can now solve the system of equations:

• q + d = 110 (Equation 1)
• 25q + 10d = 2030 (Equation 2)

Multiply Equation 1 by 10 to make the coefficients of d in both equations the same:

• 10q + 10d = 1100 (Equation 3)

Subtract Equation 3 from Equation 2 to eliminate d:

• 15q = 930
• q = 62

Substitute q back into Equation 1 to find d:

• 62 + d = 110
• d = 48

Therefore, Cassie's piggy bank contains 62 quarters and 48 dimes.