Question

Jonathan counted the money in his piggy bank. He had only quarters and dimes. When he added up his​ money, he had 25 coins worth a total of ​$3.25. How many coins of each kind did he​ have?

Answer 1

Let \( q \) be the number of quarters and \( d \) be the number of dimes. According to the problem, we have the following two equations based on the information provided:

1. The total number of coins:
\[
q + d = 25
\]

2. The total value of the coins in dollars (where quarters are worth $0.25 and dimes are worth $0.10):
\[
0.25q + 0.10d = 3.25
\]

To eliminate the decimals in the second equation, multiply the entire equation by 100:
\[
25q + 10d = 325
\]

Now we have the system of equations:
1. \( q + d = 25 \)
2. \( 25q + 10d = 325 \)

We can solve this system using substitution or elimination. Let's use the first equation to substitute for \( d \):
\[
d = 25 - q
\]

Now, substitute \( d \) in the second equation:
\[
25q + 10(25 - q) = 325
\]

Distribute the 10:
\[
25q + 250 - 10q = 325
\]

Combine like terms:
\[
15q + 250 = 325
\]

Subtract 250 from both sides:
\[
15q = 75
\]

Now, divide by 15:
\[
q = 5
\]

Now that we have \( q \), substitute it back into the equation for \( d \):
\[
d = 25 - q = 25 - 5 = 20
\]

Thus, Jonathan has:
- \( 5 \) quarters
- \( 20 \) dimes

To verify, we can check the total value:
- Value of quarters: \( 5 \times 0.25 = 1.25 \) dollars
- Value of dimes: \( 20 \times 0.10 = 2.00 \) dollars
- Total value: \( 1.25 + 2.00 = 3.25 \) dollars, which is correct.

Therefore, the final answer is:
- **5 quarters and 20 dimes.**