The expression 1, point, 1, 1, left parenthesis, 0, point, 9, 5, p, right parenthesis1.11(0.95p) represents the total amount Marques paid for a jacket originally priced pp dollars. Which changes to the original price could have resulted in this expression?

Answer
Multiple Choice Answers
A discount of 0.05% and then 111% sales tax
Sales tax of 11% and then a discount of 5%
Sales tax of 0.11% and then a discount of 0.95%
Sales tax of 111% and then a discount of 95%

1 answer

To analyze the expression \( 1.11(0.95p) \) that represents the total amount Marques paid for a jacket originally priced at \( p \) dollars, let's break it down.

  1. The expression \( 0.95p \) indicates that Marques received a discount. Specifically, applying a factor of \( 0.95 \) means that the price was reduced by \( 5% \) (which is 100% - 95%).

  2. After applying this discount, Marques ended up with \( 0.95p \) as the new price.

  3. The expression then multiplies this discounted price by \( 1.11 \). This factor indicates that a sales tax was applied to the discounted price. A multiplier of \( 1.11 \) means an additional \( 11% \) in sales tax was added (which is 100% + 11%).

So, to summarize:

  1. Marques received a discount of \( 5% \) on the original price \( p \), resulting in \( 0.95p \).
  2. Then, he paid \( 11% \) sales tax on that discounted price.

Now let's evaluate the multiple-choice options based on this analysis:

  • A: Discount of 0.05% and then 111% sales tax - Incorrect
  • B: Sales tax of 11% and then a discount of 5% - Incorrect (the order is reversed)
  • C: Sales tax of 0.11% and then a discount of 0.95% - Incorrect (mischaracterizes the tax and discount)
  • D: Sales tax of 111% and then a discount of 95% - Incorrect (mischaracterizes the tax and discount)

None of the provided answer choices accurately match the described changes to the original price. The actual changes we derived are a discount of 5% followed by a sales tax of 11%. Thus, the correct answer is not listed among the options.