- Represent the original price as \(P\) and the discount rate as \(15\% = 0.15\).
- Calculate the discount amount as \(0.15 \times P\).
- Subtract the discount amount from the original price to get the discount price: \(D = P - 0.15P\).
- Factor out \(P\) to get the final expression: \(D = P(1 - 0.15)\).
- The correct option is \(\boxed{\text{a}}\).
Explanation
- Analyzing the Discount Calculation
We are given that a pizza shop offers a 15% discount to specific customers. We want to identify the correct formula for the discount price based on the original price. Let the original price of the pizza be denoted by \(P\) and the discount price be denoted by \(D\). A 15% discount means that we subtract 15% of the original price from the original price itself. Expressing 15% as a decimal, we get \(0.15\). The discount amount is then \(0.15 \times P\).
- Formulating the Equation for Discount Price
To calculate the final discount price \(D\), we subtract the discount amount from the original price \(P\). The equation is:
\[D = P - 0.15P\]
To simplify this expression, we factor out \(P\) from the right-hand side of the equation:
\[D = P(1 - 0.15)\]
This shows that the discount price is equal to the original price multiplied by the factor \((1 - 0.15)\).
- Selecting the Correct Option
Comparing our derived formula \(D = P(1 - 0.15)\) with the options provided:
A\(\text{Discount Price} = (\text{Original Price})(1 - 0.15)\) - This matches our derivation.
B\(\text{Discount Price} = 1 - (\text{Original Price})(0.15)\) - This is incorrect.
C\(\text{Discount Price} - \text{Original Price} = 15\%\) - This is incorrect because it relates price to a percentage without the original price.
Therefore, option a is the correct representation.
Examples
Understanding how to calculate discounts is a fundamental skill in everyday shopping. For example, if you are buying a meal for \(\$20\) and there is a 15% discount, you can calculate the savings as \(\$20 \times 0.15 = \$3\), and subtract that from the total to pay \(\$20 - \$3 = \$17\). Alternatively, using the formula \(\text{Discount Price} = \text{Original Price} \times (1 - 0.15)\), you calculate \(\$20 \times 0.85 = \$17\). This method is quick and useful for quickly estimating final costs during sales or promotions.