The expression 1, point, 0, 9, left parenthesis, 0, point, 8, 5, p, right parenthesis1.09(0.85p) represents the total amount Houa paid for a jacket originally priced pp dollars. Which changes to the original price could have resulted in this expression?

Answer 1

To understand what changes to the original price \( p \) might have resulted in the expression \( 1.09(0.85p) \), let's break it down:

1. Distributing the Multiplication: The expression can be expanded: \[ 1.09(0.85p) = 1.09 \times 0.85 \times p \]

2. Calculate \( 1.09 \times 0.85 \): \[ 1.09 \times 0.85 = 0.9265 \]

3. Rewriting the Expression: The expression now can be rewritten as: \[ 0.9265p \]

This means that the total amount Houa paid is \( 0.9265 \) times the original price \( p \) of the jacket.

4. Interpretation:

   • The factor \( 0.9265 \) indicates a final price that is approximately \( 92.65% \) of the original price \( p \).
   • This signifies that there was likely a discount applied to the jacket before taxes or fees were added.

5. Determining the Discount:

   • If we find out what percentage of the original price \( p \) the payment represents, we can find a likely discount.
   • The amount \( 0.9265p \) suggests that Houa effectively paid about \( 92.65% \) of the jacket's price after a certain discount.

If we denote the original price \( p \), and let \( d \) be the discount percentage offered on the jacket, then we can express the final price paid as: \[ (1 - \frac{d}{100})p \quad \text{(where \( \frac{d}{100} \) is the decimal form of the discount)} \]

Since: \[ (1 - \frac{d}{100}) = 0.9265 \] We can solve for \( d \): \[ \frac{d}{100} = 1 - 0.9265 = 0.0735 \implies d = 0.0735 \times 100 \approx 7.35% \]

In summary, the expression \( 1.09(0.85p) \) likely indicates that the original price \( p \) of the jacket had undergone approximately a 7.35% discount before the total amount paid was calculated, factoring in some additional charges (possibly tax, indicated by the \( 1.09 \) multiplier).