The expression 1, point, 1, 2, left parenthesis, 0, point, 5, p, right parenthesis1.12(0.5p) represents the total amount Adriel paid for a jacket originally priced pp dollars. Which changes to the original price could have resulted in this expression?

Question

Answer
Multiple Choice Answers
A discount of 50% and then 112% sales tax
A discount of 0.5% and then 12% sales tax
A discount of 0.5% and then 0.12% sales tax
A discount of 50% and then 12% sales tax

Answer 1

To analyze the expression \( 1.12(0.5p) \), we can break it down:

1. Discount of 50%: If the jacket originally costs \( p \), a discount of 50% would reduce the price to: \[ 0.5p \]

2. Sales Tax of 12%: When we apply sales tax of 12% to this discounted price, it means we take 112% of that new price. The total amount paid after tax will be: \[ 1.12 \times (0.5p) \]

This matches the given expression \( 1.12(0.5p) \), which means the steps are indeed:

• Apply a 50% discount to the original price to get \( 0.5p \).
• Then, apply a 12% sales tax (which is represented as multiplying by 1.12).

Now let's evaluate the other options:

• A discount of 0.5% and then 12% sales tax: This would change the original price \( p \) to \( 0.995p \), and after a 12% sales tax, it would become \( 1.12(0.995p) \), which does not match our expression.

• A discount of 0.5% and then 0.12% sales tax: A discount of 0.5% makes the jacket cost \( 0.995p \) and applying 0.12% sales tax (which is \( 1.0012 \)) gives \( 1.0012(0.995p) \), which does not match.

• A discount of 50% and then 12% sales tax: As explained earlier, this leads to \( 1.12(0.5p) \).

Thus, the correct answer is:

A discount of 50% and then 12% sales tax.