During a sale, a music store is selling all drum kits for 20% off. Preferred customers also receive an additional 15% off.
1. Write a composite function to represent the final cost of a kit that originally cost c dollars.
2. Find the cost of a drum kit priced at $248 that a preferred customer wants to buy.
5a) g(c)= c-0.2c which means 0.8c
f(c)= c-0.15c which means 0.85c
Then you find the composition of
g(f(c))= g (0.85)
= 0.8 (0.85)
= 0.68c
5b) use 0.68c
= 0.68(248)
= $168.64
1. To find the final cost of a drum kit that originally cost c dollars, we can use the composite function:
f(c) = (1 - 0.20) * (1 - 0.15) * c
In this composite function, (1 - 0.20) represents the 20% discount during the sale, and (1 - 0.15) represents the additional 15% discount for preferred customers. These discounts are multiplied together and then multiplied by the original price c to find the final cost.
2. To find the cost of a drum kit priced at $248 that a preferred customer wants to buy, we can substitute c = 248 into the composite function:
f(248) = (1 - 0.20) * (1 - 0.15) * 248
First, we calculate the 20% discount during the sale:
0.20 * 248 = 49.6
Then, we calculate the discounted price:
248 - 49.6 = 198.4
Next, we calculate the additional 15% discount for the preferred customer:
0.15 * 198.4 = 29.76
Finally, we subtract the additional discount from the discounted price to find the final cost:
198.4 - 29.76 = 168.64
Therefore, the cost of the drum kit for the preferred customer would be $168.64.
To represent the final cost of a drum kit after the sale, we can use the following steps:
1. Calculate the price after the first discount of 20% off:
- Multiply the original price (c dollars) by 0.8 (100% - 20% = 80%).
2. Calculate the price after the additional discount of 15% off for preferred customers:
- Multiply the discounted price from step 1 by 0.85 (100% - 15% = 85%).
Now, let's write the composite function to represent the final cost of the drum kit:
1. Composite function:
f(x) = (x * 0.8) * 0.85
To find the cost of a drum kit priced at $248 that a preferred customer wants to buy, we can plug in the value of x as $248 into the composite function:
2. Cost of the drum kit after discounts:
f(248) = (248 * 0.8) * 0.85
Now, let's calculate the final cost of the drum kit:
f(248) = (248 * 0.8) * 0.85
= 198.4 * 0.85
= $168.44
Therefore, the cost of the drum kit that the preferred customer wants to buy is $168.44.