To determine the original price of each watch, we need to follow a series of steps. Here’s a detailed breakdown:
1. Understand the Information Given:
- Total amount Jayden paid after discount: [tex]$255
- Discount percentage: 15%
- Number of watches: 5
2. Calculate the Original Total Price Before the Discount:
The relationship between the total amount paid, the discount percentage, and the original total price can be represented as:
\[
\text{Total Paid} = \text{Original Total Price} \times (1 - \text{Discount Percentage})
\]
Where:
- Total Paid = $[/tex]255
- Discount Percentage = 15% or 0.15 in decimal
We can rearrange this formula to solve for the original total price:
[tex]\[
\text{Original Total Price} = \frac{\text{Total Paid}}{1 - \text{Discount Percentage}}
\][/tex]
Plug in the values:
[tex]\[
\text{Original Total Price} = \frac{255}{1 - 0.15}
\][/tex]
[tex]\[
\text{Original Total Price} = \frac{255}{0.85}
\][/tex]
[tex]\[
\text{Original Total Price} = 300
\][/tex]
3. Calculate the Original Price per Watch:
Now that we know the original total price for 5 watches is [tex]$300, we can find the price per individual watch by dividing the original total price by the number of watches:
\[
\text{Original Price per Watch} = \frac{\text{Original Total Price}}{\text{Number of Watches}}
\]
\[
\text{Original Price per Watch} = \frac{300}{5}
\]
\[
\text{Original Price per Watch} = 60
\]
Therefore, the original price of each watch was $[/tex]60.
