You make a purchase at a local hardware store, but what you've bought is too big to take home in your car. For a small fee, you arrange to have the hardware store deliver your purchase for you. You pay for your purchase, plus the sales taxes, plus the fee. The taxes are 7.5% and the fee is $20. (i) Write a function t(x) for the total, after taxes, on the purchase amount x. Write another function f(x) for the total, including the delivery fee, on the purchase amount x. (ii) Calculate and interpret (f o t)(x) and (t o f )(x). Which results in a lower cost to you

Explanation:

Given

-- delivery

Solving (a): The function for total cost, after tax.

This is calculated as:

Where:

total purchase

So, we have:

Solving (b): Include the delivery fee

Solving (c): (f o t)(x) and (t o f)(x)

We have:

So:

This gives:

Expand

So:

We have:

So:

This gives:

We have:

---- This represents the function to pay tax on the item and on the delivery

--- This represents the function to pay tax on the item only

The x coefficients in both equations are equal.

So, we compare the constants

means that (t o f)(x) has a lower cost

the answer would be 2

since they are only saying that the couple has 20 daughters and so on but they never said that they went to the movies as well therefore the couple was the only people that went to the movies.

hope this ! : 3

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