Let the number of quarters be \( q \). Since Afton has four times as many dimes as quarters, the number of dimes is \( 4q \).
Next, we calculate the total value of the quarters and dimes:
- The value of the quarters is given by \( 0.25q \) (since each quarter is worth 25 cents).
- The value of the dimes is given by \( 0.10(4q) = 0.40q \) (since each dime is worth 10 cents).
We can sum these values to find the total value that Afton has:
\[ 0.25q + 0.40q = 14.95 \]
Combining the terms gives:
\[ 0.65q = 14.95 \]
To find \( q \), we divide both sides by 0.65:
\[ q = \frac{14.95}{0.65} \]
Now let's calculate it:
\[ q = \frac{14.95 \times 100}{65} = \frac{1495}{65} = 23 \]
So, Afton has \( \boxed{23} \) quarters.
To verify, we can calculate the number of dimes:
\[ 4q = 4 \times 23 = 92 \]
Now, let's check the total value:
- Value of quarters: \( 23 \times 0.25 = 5.75 \) dollars
- Value of dimes: \( 92 \times 0.10 = 9.20 \) dollars
Adding these two amounts together:
\[ 5.75 + 9.20 = 14.95 \text{ dollars} \]
The calculation is correct, confirming that Afton has \( \boxed{23} \) quarters.