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.
248 - .2(248) - .15(248-.2(248)) = ?
To find the final cost of a drum kit that originally cost c dollars, given the sale discount of 20% and additional discount of 15% for preferred customers, we can write a composite function.
1. First, we find the price after the 20% discount. This means the price is reduced by 20 percent of the original price, which is given as c. The formula for this is:
Discounted price after 20% off = c - (20/100) * c = c - 0.2c = 0.8c
2. Next, we find the price after the additional 15% discount for preferred customers. This discount is applied to the discounted price from step 1. The formula for this is:
Discounted price after additional 15% off = (0.8c) - (15/100) * (0.8c) = 0.8c - 0.12c = 0.68c
So, the composite function representing the final cost of a drum kit is:
f(c) = 0.68c
Now, we can substitute the original price given as c = 248 dollars to find the final cost for a preferred customer purchasing the drum kit:
f(248) = 0.68 * 248
Calculating the above expression, the cost of a drum kit priced at 248 dollars that a preferred customer wants to buy is approximately 168.64 dollars.