SOLUTION: You make a purchase at a local furniture store, but what you bought is too big to take home in your car. You arrange to have the store deliver your purchase for you, for an extra f

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: You make a purchase at a local furniture store, but what you bought is too big to take home in your car. You arrange to have the store deliver your purchase for you, for an extra f      Log On


   

Question 1193281: You make a purchase at a local furniture store, but what you bought is too big to take home in your car. You arrange to have the store deliver your purchase for you, for an extra fee. You pay for your purchase + the sales tax + the fee. The sales tax is 5% and the delivery fee is $50.
a. Write a function a(x) for the total after taxes, on the purchase amount x. Write another function b(x) for the total before taxes including the delivery fee, on the purchase amount x.
b. Calculate and interpret (b(a(x)) and (a(b(x)). Which method of determining price results in a lower cost to you?
c. Suppose that taxes, by law, are not to be charged on delivery fees. Which composite function must then be used.
Answer by Scott713(2) About Me  (Show Source):
You can put this solution on YOUR website!
A. a%28x%29=x%2A1.05 is the total, after taxes, on the purchase amount "x", not including the delivery fee in any way.
b%28x%29=x%2B50 is the total, before taxes, of the purchase amount and the delivery fee.
B. b%28a%28x%29%29=b%28x%2A1.05%29=%28x%2A1.05%29%2B50
a%28b%28x%29%29=a%28x%2B50%29=%28x%2B50%29%2A1.05=%28x%2A1.05%29%2B%2850%2A1.05%29
b(a(x)) is the lower cost because tax is not assessed on the delivery fees, which would add $2.50 to the total.
C. b(a(x)) would be used
Note: multiplying a number by 1.05 gives you the number plus 5% of the number. Multiplying by just 0.05 would give you just the 5%