The expression given is \( 1.11(0.95p) \). To understand what changes to the original price \( p \) could lead to this expression, let's break it down:
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Understanding the components:
- The \( 0.95p \) part suggests that Marques received a discount on the original price \( p \). Specifically, \( 0.95p \) indicates that he paid 95% of the original price, which means he received a 5% discount.
- The \( 1.11 \) part means that after this discount, there’s an additional charge - a 11% increase in the price of the discounted amount.
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Interpreting the operation:
- The sequence is first applying the discount and then applying an increase to the discounted price:
- \( 0.95p \): original price \( p \) reduced by 5%.
- Then multiplying by \( 1.11 \): this increases the new price by 11%.
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Final formulation:
- Thus, the overall operation can be summarized as: \[ \text{Final Price} = 1.11 \times (0.95p) = 1.11 \cdot 0.95 \cdot p \]
- Calculating \( 1.11 \cdot 0.95 \) gives \( 1.0545 \), which means that the total price Marques paid is approximately \( 1.0545p \).
From this analysis we can conclude:
- Marques got a 5% discount on the original price \( p \).
- After the discount, a 11% increase was applied to the discounted price of the jacket.
The final price Marques paid can be interpreted as an effective increase from the original price of approximately 5.45%.
So, the changes to the original price that resulted in the expression \( 1.11(0.95p) \) were:
- A 5% discount followed by an 11% increase on the discounted price.
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