A discount clothing store buys shirts and slacks with a list price of \( \$ 12,750 \). If the wholesaler offers trade discounts of \( 15 / 25 / 15 \), find the single equivalent discount. Select one: a. 444375 b. .357896 c. 458125 d. .352852

To determine the single equivalent discount for the sequential trade discounts of \(15\% / 25\% / 15\), follow these steps: 1. **Understand Sequential Discounts:** - When discounts are applied sequentially, each discount is applied to the price after the previous discount has been deducted. 2. **Calculate the Remaining Price After Each Discount:** - After the first discount of \(15\%\): \[ \text{Remaining Price} = 1 - 0.15 = 0.85 \quad (85\%) \] - After the second discount of \(25\%\): \[ \text{Remaining Price} = 0.85 \times (1 - 0.25) = 0.85 \times 0.75 = 0.6375 \quad (63.75\%) \] - After the third discount of \(15\%\): \[ \text{Remaining Price} = 0.6375 \times (1 - 0.15) = 0.6375 \times 0.85 = 0.541875 \quad (54.1875\%) \] 3. **Determine the Total Single Equivalent Discount:** - The total remaining price after all discounts is \(54.1875\%\). - Therefore, the total discount is: \[ 1 - 0.541875 = 0.458125 \quad (45.8125\%) \] 4. **Match with the Given Options:** - The calculated single equivalent discount is \(45.8125\%\), which corresponds to option **c. 458125**. **Answer:** **c. 458125**