SOLUTION: The suggested retail price of a new car is p dollars. The dealership advertised a factory rebate of $1200 and an 8% discount. a) Write a function R in terms of p, giving the cost

Question 164174: The suggested retail price of a new car is p dollars. The dealership advertised a factory rebate of $1200 and an 8% discount.
a) Write a function R in terms of p, giving the cost of the car after receiving the rebate from the factory.
b) Write a function S in terms of p, giving the cost of the car after receiving the dealership discount.
c) Form the composite functions [(R)(S)]p and [(S)(R)]p and interpret each.
d) Find [(R)(S)](18,400)and [(S)(R)]18,400. Which yields the lower cost for the car? Explain

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Answer by aka042(26) (Show Source): You can put this solution on YOUR website!
a)The cost of a car after receiving the rebate from the factory is the cost of the car minus the fixed $1200 rebate. Therefore, R = p - 1200.

b)The cost of a car after receiving the dealership discount is the cost of the car less 8% of the cost of the car. Therefore, S = (1-.08)*p, or S=(.92)*p.

c)The composite function [(R)(S)]p is found by plugging in S into p in the R equation. So we have [(R)(S)]p = (.92)*p - 1200. We interpret this as the dealership discount being applied to the price of the car BEFORE the factory discount is taken. Similarly, the compositive function [(S)(R)]p is found by plugging in R into p in the S eqution. So we have [(S)(R)]p = (.92)*(p-1200). We interpret this as the dealership discount being applied to the price of the car AFTER the factory discount is taken.

d)[(R)(S)](18,400) is found by plugging in 18,400 into our [(R)(S)]p equation. So we have [(R)(S)]18400 = (.92)*18400 - 1200 = 15728. Similarly, [(S)(R)](18400) is found by plugging in 18,400 into our [(S)(R)]p equation. So we have [(S)(R)](18400) = (.92)(18400-1200) = (.92)(17200) = 15824.

To test your understanding, ask yourself this: which composite function do you think the dealer would prefer to use? What about the person buying the car? Does your answer hold true no matter what the price of the car?
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