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.