Question

You are looking for a new refrigerator at Kitchens-R-Us and will need to have it delivered. In order to stick to your budget, you must remember that the current tax rate is 7.8% and also factor in the $65 delivery fee.a. Write a function () to model the total price of the refrigerator, including tax.b. Since you need to have it delivered, you must include the $65 delivery fee. Write a function ()that models the original price of the refrigerator and the fee, excluding tax.c. In order to budget a final price, you must include the price of the refrigerator, tax and delivery fee. Find the functions (()) (()). Which option is cheaper?d. If state law prohibits taxes to be added to a delivery fee, which of your functions is compliant with the law?Situation #2You 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) = 1.078x (considering that the 7.8% tax (0.078) is added to the price, x.

b) D(x) = x + 65 (the delivery fee is $65)

c) P(D(x)) = P(x+65) = 1.078(x + 65) = 1.078x + 70.07

D(P(x)) = D(1.078x) = 1.078x + 65

D(P(x)) is cheaper, as 65 < 70.07

If there's the law, P(D(x)) will be complaint. Because in it, the tax is being added to the delivery fee.