During a sale, a music store is selling all drum kits for 20 percent off. Preferred customers also receive an additional fifteen percent off. Write a composite function to represent the final cost of a kit that originally cost c dollars. Find the cost of a drum kit price at 248 dollars that a preferred customer wants to buy.
To write a composite function to represent the final cost of a drum kit, we need to break down the discounts step by step.
Step 1: Apply the 20% off discount.
The drum kit is initially priced at c dollars. After a 20% off discount, the cost is reduced by 20/100 * c = 0.20c dollars.
Step 2: Apply the additional 15% discount for preferred customers.
After the initial discount, the cost is now (c - 0.20c) dollars. To apply the additional 15% off discount, the cost is further reduced by 15/100 * (c - 0.20c) = 0.15(c - 0.20c) = 0.15(0.80c) dollars.
Combining these steps, we can write the composite function as follows:
f(c) = (1 - 0.20)(1 - 0.15)c = 0.80 * 0.85c.
Now, let's calculate the final cost of a drum kit priced at 248 dollars that a preferred customer wants to buy:
f(248) = 0.80 * 0.85 * 248
= 0.68 * 248
≈ 168.64 dollars.
Therefore, the cost of the drum kit that a preferred customer wants to buy is approximately 168.64 dollars.