Question

A coin bank has 250 coins, dimes and quarters, worth $39.25. How many of each type of coin are there?

Answer 1

Let's denote the number of dimes as \( d \) and the number of quarters as \( q \).

We have the following two equations from the problem statement:

1. The total number of coins:
\[
d + q = 250
\]

2. The total value of the coins (in cents):
\[
10d + 25q = 3925
\]
(Note: The value in dollars is converted to cents for easier calculations.)

Now we can solve these equations step-by-step.

From the first equation, we can express \( q \) in terms of \( d \):
\[
q = 250 - d
\]

Next, we substitute \( q \) into the second equation:
\[
10d + 25(250 - d) = 3925
\]

Expanding the equation:
\[
10d + 6250 - 25d = 3925
\]

Combining like terms:
\[
-15d + 6250 = 3925
\]

Now, let's isolate \( d \):
\[
-15d = 3925 - 6250
\]
\[
-15d = -2325
\]

Dividing both sides by -15:
\[
d = \frac{2325}{15} = 155
\]

Now that we have \( d \), we can find \( q \):
\[
q = 250 - d = 250 - 155 = 95
\]

Thus, the number of dimes is \( d = 155 \) and the number of quarters is \( q = 95 \).

Let's summarize:
- Number of dimes: 155
- Number of quarters: 95

We can double-check the values:

Calculating the total value:
- Value from dimes: \( 155 \times 10 = 1550 \) cents
- Value from quarters: \( 95 \times 25 = 2375 \) cents
- Total value: \( 1550 + 2375 = 3925 \) cents (which corresponds to $39.25)

Everything checks out correctly. Therefore, the solution is:

- **Dimes:** 155
- **Quarters:** 95