The expression given is \( 1.12(0.85p) \), representing the total amount Aaliyah paid for a jacket originally priced at \( p \) dollars. To analyze the expression, let's break it down:
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Understanding the Components:
- The term \( 0.85p \) indicates that the original price of \( p \) dollars was discounted by 15%, since multiplying by \( 0.85 \) means Aaliyah paid 85% of the original price.
- The term \( 1.12 \) suggests that after the discount, Aaliyah is also charged an additional 12% in tax on the discounted price.
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Calculating the Total Amount: \[ \text{Discounted Price} = 0.85p \] \[ \text{Total Amount Paid} = 1.12 \times (0.85p) = 0.95p \] This shows that Aaliyah effectively pays 95% of the original price of the jacket when considering the discount and the tax together.
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Changes to the Original Price: To arrive at the expression \( 1.12(0.85p) \), Aaliyah could have undergone the following changes to the original price:
- The jacket initially had a price of \( p \) dollars.
- A discount of 15% was applied, changing the price to \( 0.85p \).
- Sales tax of 12% was then applied to the discounted price, increasing it from \( 0.85p \) to \( 1.12 \times 0.85p \).
In summary, the changes that resulted in the expression \( 1.12(0.85p) \) involved a 15% discount from the original price followed by a 12% tax on the discounted price.
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