Question
What is the original price of the jacket if Adriel paid $1.12(0.5p) for it, and the expression represents the total amount paid after applying a discount and sales tax?
Answers
GPT-4o mini
To find the original price of the jacket (denoted as \( p \)), we can analyze the given expression \( 1.12(0.5p) \).
1. **Understand the Expression**:
- The term \( 0.5p \) suggests that Adriel received a 50% discount on the original price \( p \), meaning he paid half of the original price.
- The factor \( 1.12 \) indicates that sales tax was applied after the discount. This means Adriel is paying 112% of the discounted price.
2. **Calculate the Total Paid**:
- The total amount Adriel paid can be expressed as:
\[
\text{Total Paid} = 1.12 \times (0.5p) = 0.56p
\]
This means Adriel paid 56% of the original price \( p \) after the discount and tax.
3. **Reverse the Expression to Find \( p \)**:
Since \( 0.56p \) represents the amount Adriel paid, we can express \( p \) in terms of the amount paid:
\[
\text{If } 0.56p = \text{Amount Paid}
\]
We can consider the scenario in which the total amount Adriel actually paid is known or is represented as \( x \) (where \( x = 1.12(0.5p) \)):
- To isolate \( p \):
\[
p = \frac{x}{0.56}
\]
4. **Conclusion**:
Without further information about the specific total amount Adriel paid in dollars, we can't calculate an exact numerical value for \( p \). However, if you know how much Adriel paid (the value of \( x \)), you can easily replace \( x \) in the formula \( p = \frac{x}{0.56} \) to find the original price.
1. **Understand the Expression**:
- The term \( 0.5p \) suggests that Adriel received a 50% discount on the original price \( p \), meaning he paid half of the original price.
- The factor \( 1.12 \) indicates that sales tax was applied after the discount. This means Adriel is paying 112% of the discounted price.
2. **Calculate the Total Paid**:
- The total amount Adriel paid can be expressed as:
\[
\text{Total Paid} = 1.12 \times (0.5p) = 0.56p
\]
This means Adriel paid 56% of the original price \( p \) after the discount and tax.
3. **Reverse the Expression to Find \( p \)**:
Since \( 0.56p \) represents the amount Adriel paid, we can express \( p \) in terms of the amount paid:
\[
\text{If } 0.56p = \text{Amount Paid}
\]
We can consider the scenario in which the total amount Adriel actually paid is known or is represented as \( x \) (where \( x = 1.12(0.5p) \)):
- To isolate \( p \):
\[
p = \frac{x}{0.56}
\]
4. **Conclusion**:
Without further information about the specific total amount Adriel paid in dollars, we can't calculate an exact numerical value for \( p \). However, if you know how much Adriel paid (the value of \( x \)), you can easily replace \( x \) in the formula \( p = \frac{x}{0.56} \) to find the original price.