To find out how much money Riley needs to earn, we first need to calculate the total cost of the jacket including the sales tax.
- Cost of the jacket: $49.99
- Sales tax rate: 725%
First, convert the sales tax percentage to a decimal by dividing by 100:
\[ 725% = \frac{725}{100} = 7.25 \]
Next, calculate the total sales tax:
\[ \text{Sales tax} = \text{Cost of the jacket} \times \text{Sales tax rate} \]
\[ \text{Sales tax} = 49.99 \times 7.25 \]
Now, calculating this gives:
\[ \text{Sales tax} = 49.99 \times 7.25 ≈ 362.43 \]
Now, add the sales tax to the original price of the jacket to get the total amount Riley needs to pay:
\[ \text{Total cost} = \text{Cost of the jacket} + \text{Sales tax} = 49.99 + 362.43 \]
\[ \text{Total cost} ≈ 412.42 \]
Rounding to the nearest dollar:
\[ \text{Total cost} \approx 412 \]
Therefore, Riley needs to earn approximately $412 to purchase the jacket.