Let's analyze the problem and determine where the employee made an error in their calculations. Here's a step-by-step breakdown of how the discount should be correctly applied versus the mistake made by the employee.
1. Correct Calculation:
- The original price of the pizza is \[tex]$12.
- The discount offered is 15%.
For a discount calculation, you subtract the discount percentage from 100% to find out what percentage of the original price the customer needs to pay.
- So, the customer pays 100% - 15% = 85% of the original price.
- Convert 85% to a decimal: 85% = 0.85.
- Calculate the discounted price:
\[
\text{Discounted Price} = \text{Original Price} \times 0.85 = 12 \times 0.85 = 10.2
\]
Therefore, the correct discounted price should be \$[/tex]10.20.
2. Employee's Error:
- The employee seems to be calculating the amount of discount to be deducted incorrectly.
- They mistakenly thought to subtract 85% from the price directly to get the discounted amount, rather than applying the 15% discount correctly.
- The employee set up the calculation as:
[tex]\[
\text{Employee's Discount} = (100\% - 85\%) \times \text{Original Price} = (15\%) \times \$12 = 0.15 \times 12 = 1.80
\][/tex]
The employee's calculation leads to a discounted amount of \[tex]$1.80 instead of the price after discount.
To further illustrate, the employee deducts 85% from 100%, giving 15%. Then, instead of calculating 85% of the original price, the employee applies 15% of the original price as the discounted price, which is entirely incorrect.
3. Correct Interpretation:
- The employee's discount method results in a discounted price of \$[/tex]1.80 but this is not the price the customer should pay, it's the amount discounted from the original price.
- Using the employee’s approach:
[tex]\[
\text{Discounted Amount} = \$12 \times 0.15 = \$1.80
\][/tex]
- Subtract this discounted amount from the original price:
[tex]\[
\text{Employee's Final Price} = \$12 - \$1.80 = \$10.20
\][/tex]
However, this roundabout and confusing method doesn't change the error made initially in the method calculation.
So, the main error is the misunderstanding of how to calculate the discount price. The employee incorrectly thought [tex]\( 15\% \)[/tex] is the amount to subtract from original rather the right discount calculation needing [tex]\((100\% - 15\%) \)[/tex]. The correct discounted price for the pizza should be \$10.20.
