Problem 21 - Prealgebra

Question

A frozen pizza is on sale at a \(25 \%\) discount. Find the sale price of the pizza if it normally sells for \(\$ 4.85\)

Step-by-Step Solution

Answer

The sale price of the pizza is $3.64.

Step 1: Understand the Discount Formula

A percentage discount means a certain percentage is taken off the original price. The formula to find the discount amount is: \( \text{Discount Amount} = \text{Original Price} \times \text{Discount Percent} \).

Step 2: Calculate the Discount Amount

Substitute the given values into the discount formula: \( \text{Discount Amount} = 4.85 \times 0.25 \). By calculating this, we find \( \text{Discount Amount} = 1.2125 \).

Step 3: Determine the Sale Price

Subtract the discount amount from the original price to find the sale price: \( \text{Sale Price} = 4.85 - 1.2125 \). This yields a sale price of \( 3.6375 \).

Step 4: Round to the Nearest Cent

Round \( 3.6375 \) to the nearest cent to get the final sale price, which is \( 3.64 \).

Key Concepts

Understanding Discount Calculation

Discounts are a way to save money by lowering the original price of an item, like in a store sale. In percentage terms, a discount tells us how much of the original price we don't have to pay. To calculate the discount, multiply the original price by the discount percent (as a decimal).
For example, if a pizza originally costs \(\$4.85\) and is on sale at a \(25\%\) discount, you first convert the discount percent into a decimal, which is \(0.25\). Then apply the formula:

• \(\text{Discount Amount} = \text{Original Price} \times \text{Discount Percent}\)
• \(\text{Discount Amount} = 4.85 \times 0.25\)

Performing this calculation, you get \(1.2125\) as the discount amount. This tells you how much less you will pay compared to the original price.

Finding the Sale Price

After finding out how much the discount saves you, you need to determine what you will actually pay, known as the sale price. To do this, you subtract the discount amount from the original price.
Using our pizza example, after calculating a discount of \(1.2125\), find the sale price with:

• \(\text{Sale Price} = \text{Original Price} - \text{Discount Amount}\)
• \(\text{Sale Price} = 4.85 - 1.2125\)

This math gives a sale price of \(3.6375\), meaning it costs less after the discount is applied but is not rounded to a typical currency format yet.

Rounding to the Nearest Cent

Once you know the unrounded sale price, it often needs adjusting to match standard currency format, which deals with whole cents. This means putting the amount in dollars and cents.
Currency is typically rounded to the nearest cent. If the thousandths digit (third decimal place) is 5 or more, round up the hundredths digit (second decimal place). If the thousandths digit is less than 5, round down.
For the pizza with an unrounded sale price of \(3.6375\):

• Look at the third decimal place: 7.
• Since 7 is more than 5, you round up the hundredths digit.
• The sale price becomes \(3.64\).

Now, you have the final sale price that customers pay at checkout, rounded to \(\$3.64\), aligning with standard practice in currency transactions.