Questions: Find the marked price and sales tax. Total price 362.79, Sales tax rate 6.9%, Marked price, Sales tax. (Round to the nearest cent.)

Solution Steps

To find the marked price and sales tax given the total price and sales tax rate, we can use the following approach:

1. Let the marked price be \( M \).
2. The sales tax is calculated as \( \text{Sales Tax} = M \times \frac{\text{Sales Tax Rate}}{100} \).
3. The total price is the sum of the marked price and the sales tax: \( \text{Total Price} = M + \text{Sales Tax} \).
4. Substitute the expression for sales tax into the total price equation and solve for \( M \).
5. Once \( M \) is found, calculate the sales tax using the formula from step 2.

We are given the total price \( T = 362.79 \) and the sales tax rate \( r = 6.9\% \).

The relationship between the total price, marked price \( M \), and sales tax can be expressed as: \[ T = M + \left( M \times \frac{r}{100} \right) \] This can be rearranged to: \[ T = M \left( 1 + \frac{r}{100} \right) \] Substituting the known values: \[ M = \frac{T}{1 + \frac{r}{100}} = \frac{362.79}{1 + 0.069} = \frac{362.79}{1.069} \approx 339.37 \]

Now that we have the marked price, we can calculate the sales tax \( S \): \[ S = M \times \frac{r}{100} = 339.37 \times 0.069 \approx 23.42 \]

Final Answer