Amanda bought a trolley luggage bag that was offered at a 20% discount off its original price of P dollars. A sales tax of t percent was applied to the discounted price, so Amanda paid a total of F dollars to the cashier. Which of the following represents t in terms of P and F?

We can represent the sales tax rate (t) in terms of P (original price) and F (total price paid) using the following equation:

**1. Discounted Price:** First, let’s find the discounted price of the luggage bag. Discount is a percentage reduction from the original price. We can calculate it as:

Discounted price = P * (1 – discount rate)

Here, the discount rate is 20% which is equivalent to 20/100 or 0.2 in decimal form.

Therefore, Discounted price = P * (1 – 0.2) = 0.8P

**2. Sales Tax and Total Price:** The sales tax (t%) is applied to the discounted price. So, the amount Amanda paid for the sales tax is:

Sales Tax amount = Discounted price * (t/100)

The total price (F) paid by Amanda is the sum of the discounted price and the sales tax amount:

F = 0.8P + Discounted price * (t/100)

**3. Isolating t:** Now, we can rearrange the equation to isolate t:

F = 0.8P + 0.8P * (t/100)

F = 0.8P (1 + t/100)

Divide both sides by 0.8P:

F / (0.8P) = 1 + t/100

Subtract 1 from both sides:

(F / (0.8P)) – 1 = t/100

Multiply both sides by 100 to express t as a percentage:

t = 100 * ((F / (0.8P)) – 1)

**Therefore, t = 100 * ((F / (0.8P)) – 1) represents the sales tax rate (t) in terms of the original price (P) and the total price paid (F).**

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