Chapter P, Problem 12E

Series Discount This is a continuation of Exercise 11. Sometimes manufacturers give more than one discount instead of a single trade discount – for example, in trading with large-volume retailers. Such a series discount is quoted as a sequence of discounts, taken one after another. Suppose a manufacturer normally gives a trade discount of $45\%$, but it has too much of the item in inventory and so wants to sell more. In this case the manufacturer may give all retailers another discount of $15\%$ and may perhaps extend yet another discount of $10\%$ to a specific retailer it wants to land as a client. In this example, the series discount would be $45\%$, $15\%$, $10\%$, calculated one after another, like this: For an item with a suggested retail price of $\$100.00$, applying the first discount gives $\$100.00-45\%\times 100.00=55.00$ dollars. The second discount of $15\%$ is applied to the $\$55.00$ as follows: $55.00-15\%\times 55.00=46.75$ dollars. Now, the third discount gives the final cost price of $\$46.75-10\%\times 46.75=42.08$ dollars.

a. Suppose an item has a suggested retail price of $\$80.00$ and the manufacturer is giving a series discount of $25\%$ and $10\%$. What is the resulting cost price?

b. Suppose an item has suggested retail price of $\$100.00$ and the manufacturer is giving a series discount of $35\%$, $10\%$, $5\%$. What is the resulting cost price?

c. What single trade discount would give the same cost price as a series of $35\%$, $10\%$, $5\%$? (Note: The answer is not $50\%$)

d. Explain why we could have calculated the same answer as in part b by multiplying $100.00\times 0.65\times 0.90\times 0.95$. In this case, what would the $0.65$, $0.90$, and $0.95$ represent?

Trade Discount Often retailers sell merchandise at a suggested retail price determined by the manufacturer. The trade discount is the percentage discount given to the retailer by the manufacturer. The resulting price is the retailers’ net cost and so is called the cost price. For example, if the suggested retail price is $\$100.00$ and the trade discount is $45\%$, then the cost price is $\$100.00-45\%\times 100=55.00$ dollars.

a. If an item has a suggested retail price of $\$9.99$ and the trade discount is $40\%$, what is the retailers’ cost price?

b. If item has a cost price of $\$37.00$ and a suggested retail price of $\$65.00$, what trade discount was used?