To solve this problem, let's denote the number of quarters Steve has as \( q \). Since he has five more dimes than quarters, we can denote the number of dimes as \( d = q + 5 \).
The value of the quarters is \( 0.25q \) dollars and the value of the dimes is \( 0.10d \) dollars. According to the problem, the total value is 74 dollars and 35 cents, which can be expressed as \( 74.35 \) dollars.
Now, we can write the equation representing the total value:
\[ 0.25q + 0.10d = 74.35 \]
Substituting \( d = q + 5 \) into the equation:
\[ 0.25q + 0.10(q + 5) = 74.35 \]
Expanding this equation:
\[ 0.25q + 0.10q + 0.50 = 74.35 \]
Combining like terms:
\[ 0.35q + 0.50 = 74.35 \]
Now, subtract \( 0.50 \) from both sides:
\[ 0.35q = 73.85 \]
Next, divide both sides by \( 0.35 \):
\[ q = \frac{73.85}{0.35} = 211 \]
Now that we have the number of quarters, we can find the number of dimes:
\[ d = q + 5 = 211 + 5 = 216 \]
Thus, Steve has:
- 211 quarters
- 216 dimes
To verify:
The total value of the quarters is:
\[ 211 \times 0.25 = 52.75 \text{ dollars} \]
The total value of the dimes is:
\[ 216 \times 0.10 = 21.60 \text{ dollars} \]
Adding these values together:
\[ 52.75 + 21.60 = 74.35 \text{ dollars} \]
The calculations confirm the solution is correct. Thus, the final answer is:
- Quarters: 211
- Dimes: 216