Question

You want to buy a shirt from your favorite clothing store. It’s on the clearance rack for 20% off! When you get to the check-out line, the store is offering two deals on top of the clearance price. Deal A allows you to take an extra 20% off the price, Deal B allows you to take $10 off the price.a. Write a function () that models the price of the shirt after the clearance discount.b. Write functions () () that model taking 20% off and $10 off the shirt, respectively, not factoring in the clearance price.c. Write functions (()) (()), which represent the prices of the shirt after the clearance price is discounted and either Deal A or Deal B is applied, respectively.d. If the original price of the shirt is $40, which is the better deal? Justify your reasoning with composition.

Answer 1

a) P(x) = 0.8x

b) A(x) = 0.8x, B(x) = x - 10

c) (()) = 0.64x, (()) = 0.8x - 10

d) deal B is the better deal

Step-by-step explanation:

a) let the original price of the shirt = x

Clearance sale of 20% = 20% (x) = 0.2(x)

discount from clearance sale = 0.2x

The price of the shirt after the clearance discount = original price - discount from clearance sale

P(x) = The price of the shirt after the clearance discount

P(x) = x - 0.2x

P(x) = 0.8x

b) let A(x) = 20% of the shirt not factoring the clearance price

Discount = 20%(x) = 0.2(x)

A(x) = x - 0.2x

A(x) = 0.8x

B(x) = $10 off the shirt not factoring the clearance price

B(x) = x - 10

c) let (()) = price of the after clearance price is discounted for deal A

Additional discount on the clearance price for deal A = 20%(0.8x) = 0.2(0.8x)

Additional discount on the clearance price for deal A = 0.16x

(()) = P(x) - Additional discount on the clearance price for deal A

(()) = 0.8x - 0.16x

(()) = 0.64x

(()) = price of the after clearance price is discounted for deal B

Additional discount on the clearance price for deal B = $10 off

Additional discount on the clearance price for deal B = P(x) - $10

(()) = 0.8x - 10

d) If original price = $40

x = 40

substitute for x in each of the deal equations we got above:

Deal A:

(()) = 0.64x = 0.64(40)

(()) = $25.56

Deal B:

(()) = 0.8x - 10 = 0.8(40) - 10

(()) = $22

$22 < $25.56

(()) < (())

Hence, deal B is the better deal

Summary:

a) We are to write the function (also known as equation) that represents the price of the shirt after the clearance discount.

This we got as P(x) = 0.8x

b) We are to write the function that shows 20% discount on the shirt without applying the clearance discount.

This we got as A(x) = 0.8x

We are to also write the function that shows $10 off the shirt without applying the clearance discount.

This we got as B(x) = x - 10

c) We are to write the function that shows 20% discount on the shirt after the clearance sale as been applied.

This we got as (()) = 0.64x

We are to write the function that shows $10 off on the shirt after the clearance sale as been applied.

This we got as (()) = 0.8x - 10

d) We are to find the better deal between A and B if the original price of the shirt is known. Original price of shirt was given as $40.

Deal A gave the price of the shirt as $25.56

Deal B gave the price of the shirt as $22

Since the price from deal B is less than the price from deal A, deal B has a better deal