Subjects business math

Racquet Cost Markup 46F663

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Stating the problem:** We need to find the original cost price of each tennis racquet before discounts, given the final selling price and two successive discounts. 2. **Understanding the discounts:** - The store purchased racquets at $57.04 each. - First discount: 44% off for buying more than 100 items. - Second discount: 33% off for purchasing in October. - Selling price to customers is $63.29. 3. **Calculating the cost price after discounts:** Let the original price be $P = 57.04$. First discount reduces price to: $$P_1 = P \times (1 - 0.44) = 57.04 \times 0.56 = 31.9424$$ Second discount reduces price further to: $$P_2 = P_1 \times (1 - 0.33) = 31.9424 \times 0.67 = 21.401808$$ So, the cost price per racquet after discounts is approximately $21.40$. 4. **Calculating markup as a percent of cost:** Markup = Selling price - Cost price $$= 63.29 - 21.401808 = 41.888192$$ Markup percent of cost: $$\frac{41.888192}{21.401808} \times 100 = 195.8\%$$ 5. **Calculating markup as a percent of selling price:** Markup percent of selling price: $$\frac{41.888192}{63.29} \times 100 = 66.2\%$$ **Final answers:** - (a) Cost price per racquet = $21.40$ - (b) Markup as percent of cost = $195.8\%$ - (c) Markup as percent of selling price = $66.2\%$