Question

Customers at the Palace Pro Shop receive a 10% discount if they are members. All customers must pay 7% in sales tax. The function f(x)=0.9x is used to determine the price of an item after the 10% member discount, where x is the regular price of the item. The function g(x)=1.07x is used to determine the total amount customers pay for a purchase after all discounts are applied. Which function can be used to determine T(x), the total amount a member pays for an item with a regular price of x dollars?

Answer 1

The total amount a member pays for an item with a regular price of x dollars is T (x) = 0.963x.

Explanation:

Key points:

• Discount is subtracted from the regular price of an item.
• Sales tax is added to the regular price of an item.

It is provided that the customers receive a 10% discount if they are members and all customers must pay 7% in sales tax.

Two functions are provided are:

f (x) = 0.90x ; the price of an item after the 10% member discount

g (x) = 1.07x ; the total amount customers pay for a purchase after sales tax is applied.

Compute the total amount a member pays for an item with a regular price of x dollars as follows:

T (x) = Discount × Sales Tax

= 0.90 × 1.07 × x

= 0.963x.

Thus, the total amount a member pays for an item with a regular price of x dollars is T (x) = 0.963x.