To find out how much money Kurt spent per month on movie streaming services, we start by converting the total expenditure into a monthly rate.
Kurt spent a total of \( 96.39 \) dollars over \( 4 \frac{1}{4} \) months. First, we need to convert \( 4 \frac{1}{4} \) months into an improper fraction or a decimal.
\[ 4 \frac{1}{4} = 4 + \frac{1}{4} = \frac{16}{4} + \frac{1}{4} = \frac{17}{4} \text{ months} \]
Next, we divide the total amount spent by the number of months to find the monthly expenditure.
\[ \text{Monthly expenditure} = \frac{\text{Total expenditure}}{\text{Total months}} = \frac{96.39}{\frac{17}{4}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ \frac{96.39}{\frac{17}{4}} = 96.39 \times \frac{4}{17} \]
Calculating the right side:
- Calculate \( 96.39 \times 4 \):
\[ 96.39 \times 4 = 385.56 \]
- Now, divide \( 385.56 \) by \( 17 \):
\[ \text{Monthly expenditure} = \frac{385.56}{17} \]
Now we perform the division:
\[ 385.56 \div 17 \approx 22.678 \]
Thus, Kurt spent approximately:
\[ \boxed{22.68} \]
dollars per month on movie streaming services (rounded to two decimal places).