Question

emily went shopping for a new video game because of a sale. the store was offering a 45% discount. if the price on the tag was p, which expression does not represent the price after the discount but before tax?

answer

○ p - 0.45p ○ 0.955p
○ 1p - 0.45p ○ 0.55p

Explanation:

Step1: Understand the discount calculation

The original price is \( p \). A 45% discount means we subtract 45% of \( p \) from \( p \). 45% of \( p \) is \( 0.45p \), so the price after discount is \( p - 0.45p \).

Step2: Simplify \( p - 0.45p \)

We can factor out \( p \): \( p(1 - 0.45) = p(0.55) = 0.55p \). Also, \( 1p - 0.45p \) is the same as \( p - 0.45p \) since \( 1p = p \).

Step3: Analyze each option

• \( p - 0.45p \): Represents original price minus discount, correct.
• \( 0.955p \): This would be a 4.5% discount (since \( 1 - 0.955 = 0.045 \) or 4.5%), not 45%, so it does not represent the price after a 45% discount.
• \( 1p - 0.45p \): Same as \( p - 0.45p \), correct.
• \( 0.55p \): Simplified form of \( p - 0.45p \), correct.

Answer:

0.955p