You are at the electronics store picking out a new television. You have a coupon for $75.00 off the price of a Samsung television and you also notice that the store is having a 15% off New Year’s Sales Event. You confirm with the store manager that the store will accept the coupon in addition to giving store discount. a. Write an equation where x is the original price of the television and c(x) is the price of the television after the $75 discount. c(x)=x-75. b. Write an equation where x is the original price of the television and p(x) is the price of the television after the 15% discount. p(x)=x-15x or p(x)=0.85x. Use the composite functions c(p(x)) (percent off then the coupon) and p(c(x)) (coupon first) to
Attached are examples to help you solve part c.
Make sure to answer all parts. Make sure to show all work and provide evidence when instructed to do so. Make sure to state your claim using a complete sentence. If stating an amount of money, you must include $.
You are at the electronics store picking out a new television. You have a coupon for $75.00 off the price of a Samsung television and you also notice that the store is having a 15% off New Year’s Sales Event. You confirm with the store manager that the store will accept the coupon in addition to giving store discount.
a. Write an equation where x is the original price of the television and c(x) is the price of the television after the $75 discount.
c(x)=x-75.
b. Write an equation where x is the original price of the television and p(x) is the price of the television after the 15% discount.
p(x)=x-15x or p(x)=0.85x.
- Use the composite functions c(p(x)) (percent off then the coupon) and p(c(x)) (coupon first) to determine which would be most beneficial to you if you purchased a Samsung television with an original price of $1,200.00. Make sure to state what the final cost would be for each situation (before sales tax). Show all work to support your answer.
Show all steps for c(p(x)) below:
The final cost of the television after applying discount (first), then coupon c(d(x)) is____
Show all steps for p(c(x)) below:
The final cost of the television_____
Hint: Which will give you a cheaper price; applying the coupon first then the % discount or applying the % discount then the coupon.
![Let's Practice
Use the equations you wrote above in a and b to answer c and d
below:
1. What would c(p(x)) mean in this situation?
first
-second
precxs) =
(x-3),9
اس
c(p(x)) = (.9x)-3
c(p(12.50)) (.9(12.50))-3 OR
(11.25) -3
$8.25
oro
(x²=3] - [(x-3)4]
(P(x)) Is the final price you will pay after applying the percent
discount first then the coupon.
2. If the original price of the cupcakes were $12.50, what would you pay
after your discounts according to the information in part 1?
c(p(x)) = (x - 10x)-3
P
C(P(12.50)) (12.50 10(12.50))-3
(12.50 -1.25) - 3
= 11.25 3
$8.25](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42d32c99-f186-4d20-877e-c0d5c559d6f0%2F2b077a61-922d-445b-bf4d-4f9111f4f9c2%2Fe02f5w_processed.jpeg&w=3840&q=75)
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