1. **Problem statement:** Par Putters Company sells golf balls for 33 per dozen. Overhead expenses are 31% of cost, and owners require 18% profit of cost. We need to find: (a) Cost price per dozen golf balls. (b) Price to cover all costs and expenses. (c) Highest markdown rate to break even. (d) Highest discount rate without loss. 2. **Define variables:** Let $C$ = cost price per dozen golf balls. Selling price $S = 33$. Overhead expenses = 31% of $C = 0.31C$. Profit required = 18% of $C = 0.18C$. 3. **Formulate the selling price:** Selling price covers cost, overhead, and profit: $$S = C + 0.31C + 0.18C = (1 + 0.31 + 0.18)C = 1.49C$$ 4. **(a) Find cost price $C$:** $$33 = 1.49C$$ Divide both sides by 1.49: $$\cancel{1.49}C = \frac{33}{\cancel{1.49}}$$ $$C = \frac{33}{1.49} \approx 22.15$$ 5. **(b) Price to cover all costs and expenses:** This is the selling price $S$ which includes cost, overhead, and profit, so: $$S = 33$$ 6. **(c) Highest markdown rate to break even:** Break even means no profit, only covering cost and overhead: Break even price $= C + 0.31C = 1.31C$ Calculate break even price: $$1.31 \times 22.15 = 29.02$$ Markdown amount: $$33 - 29.02 = 3.98$$ Markdown rate: $$\frac{3.98}{33} \approx 0.1206 = 12.06\%$$ 7. **(d) Highest discount rate without loss:** No loss means price must be at least cost price $C = 22.15$ Discount amount: $$33 - 22.15 = 10.85$$ Discount rate: $$\frac{10.85}{33} \approx 0.3288 = 32.88\%$$ **Final answers:** (a) Cost price per dozen golf balls is approximately 22.15. (b) Price to cover all costs and expenses is 33. (c) Highest markdown rate to break even is approximately 12.06%. (d) Highest discount rate without loss is approximately 32.88%.