Fresh Market prepares gourmet dinners each day. On Wednesday, 80 baked chicken dinners were made at a cost of \( \$ 3.50 \) each. A \( 10 \% \) spoilage rate in anticipated. At what selling price should the dinners be sold to acheive a \( 60 \% \) markup based on selling price? Select one: a. \( \$ 280.00 \) b. \( \$ 8.75 \) c. \( \$ 7.88 \) d. \( \$ 9.72 \)
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To solve this problem, we first need to account for the spoilage. With 80 dinners and a 10% spoilage rate, the number of dinners that will actually be sold is: \( 80 \times (1 - 0.10) = 72 \) dinners. Next, calculate the total cost of the dinners: \( 80 \text{ dinners} \times \$3.50 = \$280.00 \). Since only 72 dinners will be sold, the cost per dinner needs to account for the total cost divided by the number sold: \( \text{Cost per dinner} = \frac{\$280.00}{72} \approx \$3.89 \). To achieve a 60% markup based on the selling price, we can use the formula: \[ \text{Selling Price} = \text{Cost} / (1 - \text{Markup Percentage}) \] Substituting the values gives us: \[ \text{Selling Price} = \$3.89 / (1 - 0.60) = \$3.89 / 0.40 = \$9.72 \]. Thus, the selling price should be \( d. \$9.72 \).