Subjects algebra

Book Selling Price 761D7B

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1. **State the problem:** We need to find the selling price of a single book so that the publisher earns a 22% profit, given that 1,250 copies are published and shipping costs R52,500. 2. **Identify the total percentage of expenses:** The pie chart percentages are Advertising 9%, Binding 12%, Printing 21%, Authoring 17%, Materials 27%, and Shipping is the remaining percentage. 3. **Calculate the Shipping percentage:** Total percentage must be 100%, so Shipping % = 100% - (9% + 12% + 21% + 17% + 27%) = 100% - 86% = 14%. 4. **Calculate the total cost of publishing all books:** Shipping cost corresponds to 14% of total expenses. Let total cost be $C$. Then: $$0.14 \times C = 52500$$ Solve for $C$: $$C = \frac{52500}{0.14} = 375000$$ So, total cost to publish 1,250 books is 375,000. 5. **Calculate cost price per book:** $$\text{Cost per book} = \frac{375000}{1250} = 300$$ 6. **Calculate selling price per book for 22% profit:** Profit = 22% of cost price, so selling price $S$ is: $$S = 300 + 0.22 \times 300 = 300 \times (1 + 0.22) = 300 \times 1.22 = 366$$ **Final answer:** The selling price of a single book should be **366** to earn a 22% profit.