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 find the final cost of a drum kit after applying a 20% discount and an additional 15% discount for preferred customers, we can use a composite function.
Let's break down the process step by step:
Step 1: Apply a 20% discount to the original price of the drum kit.
To do this, we multiply the original price (c dollars) by 0.80 (1 - 20% or 0.20):
Original Price after 20% discount = c * 0.80
Step 2: Apply an additional 15% discount for preferred customers.
To calculate the final price, we multiply the price after the 20% discount by 0.85 (1 - 15% or 0.15):
Final Price = (c * 0.80) * 0.85
Now, let's write the composite function to represent the final cost of the drum kit:
f(c) = (c * 0.80) * 0.85
To find the cost of a drum kit priced at $248 that a preferred customer wants to buy, we replace c with 248 in the composite function:
f(248) = (248 * 0.80) * 0.85
Calculating:
f(248) = 198.4 * 0.85
f(248) = 168.44
Therefore, the final cost of the drum kit that the preferred customer wants to buy, originally priced at $248 after applying the 20% and 15% discounts, is $168.44.