Series discount: This is a continuation. 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% × 100.00 = 55.00 dollars. The second discount of 15% is applied to the $55.00 as follows: 55.00 − 15% × 55.00 = 46.75 dollars. Now the third discount gives the final cost price of 46.75 − 10% × 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 a 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 discount 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 × 0.65 × 0.90 × 0.95 .
In this case, what do the 0.65, 0.90, and 0.95 represent?