Question

A furniture store is having a weekend sale and is offering a 20% discount on patio chairs and tables. The sales tax on furniture is 6.25%. Using function composition, how can you represent the total amount, A, that you would need to pay for furniture that costs x dollars?

Answer 1

P(x)=0.085x

Explanation:

Let the cost of the item be x

Discount = 20% of x

We know that 20%=
`(20)/(100)`

Hence

Discount = 0.02x

Selling Price = x - 0.02x

Selling Price = 0.08x

Tax = 6.25% of Selling price

Tax = 0.0625*(0.08)x

Tax=0.005x

Net payment to be made = selling price + Tax

Net Payment = 0.08x+0.005x

Net payment = 0.085x

Hence we can write our function as

P(x)=0.085x

Answer 2

First, we subtract 20% of the amount from x, so the initial cost of the furniture should be 80% of x or 0.80x. Then, due to the sales taxs, this amount should be added with 6.25% of itself. Such that,
A = 0.80x + 0.0625(0.80x)
= 0.85x