Question

dante had 27 coins that are all dimes and quarters. the value of the coins is 4.35. how many dimes and how many quarters does dante have.

Answer 1

Let \( d \) represent the number of dimes and \( q \) represent the number of quarters. We can set up the following equations based on the information given in the problem:

1. The total number of coins:
\[
d + q = 27
\]

2. The total value of the coins (in dollars):
\[
0.10d + 0.25q = 4.35
\]

To simplify calculations, we can multiply the second equation by 100 to eliminate the decimals:
\[
10d + 25q = 435
\]

Now we have the following system of equations:
1. \( d + q = 27 \)
2. \( 10d + 25q = 435 \)

We can solve the first equation for \( d \):
\[
d = 27 - q
\]

Now we can substitute \( d \) in the second equation:
\[
10(27 - q) + 25q = 435
\]

Expanding this, we get:
\[
270 - 10q + 25q = 435
\]
\[
270 + 15q = 435
\]

Now, we can isolate \( q \):
\[
15q = 435 - 270
\]
\[
15q = 165
\]
\[
q = \frac{165}{15} = 11
\]

Now that we have \( q \), we can find \( d \):
\[
d = 27 - q = 27 - 11 = 16
\]

Thus, Dante has:
- **16 dimes**
- **11 quarters**

Let's verify if the values are correct:

- Value of 16 dimes:
\[
16 \times 0.10 = 1.60
\]

- Value of 11 quarters:
\[
11 \times 0.25 = 2.75
\]

- Total value:
\[
1.60 + 2.75 = 4.35
\]

The calculations are correct. Therefore, Dante has **16 dimes and 11 quarters**.