Problem 22 - Prealgebra

Question

Suppose a video game is on sale at a \(15 \%\) discount. If it normally sells for \(\$ 29.99,\) what is the sale price?

Step-by-Step Solution

Answer

The sale price is $25.49.

Step 1: Understand the Percent Discount

The discount given is a percentage of the original price. In this case, it's 15% of the normal selling price. We need to convert this percentage into a decimal for calculation purposes. By dividing 15 by 100, we get 0.15.

Step 2: Calculate the Discount Amount

Multiply the original price by the decimal form of the discount percentage to find the discount amount. \[\text{Discount Amount} = 29.99 \times 0.15\]

Step 3: Perform the Multiplication

Calculate the discount amount:\[29.99 \times 0.15 = 4.4985\]Since we deal with currency, round to two decimal places: Thus, the discount amount is approximately $4.50.

Step 4: Calculate the Sale Price

Subtract the discount amount from the original price to find the sale price:\[\text{Sale Price} = 29.99 - 4.50\]

Step 5: Perform the Subtraction

Perform the subtraction to find the sale price:\[29.99 - 4.50 = 25.49\]

Step 6: Conclusion

Thus, the sale price of the video game, after applying the 15% discount, is $25.49.

Key Concepts

Understanding Discount Calculation

Percentage discount involves reducing the original price of an item by a certain percentage, offering buyers a better deal. To perform a discount calculation, you begin by changing the percentage into a decimal. This is done by dividing the percentage by 100. For example:

• 15% discount → 15 ÷ 100 = 0.15

Once you have the decimal, multiply it by the original price to determine the discount amount. In our example:

• Discount Amount = Original Price × Decimal Percentage
• Discount Amount = $29.99 × 0.15
• Discount Amount = $4.4985

The decimal value helps in accurately calculating the discount to be subtracted from the original price.

Finding the Sale Price Calculation

After determining the discount amount, the next step is to find the sale price. Subtract the discount amount from the original price:

• Sale Price = Original Price - Discount Amount
• Sale Price = $29.99 - $4.50
• Sale Price = $25.49

This calculation ensures you are correctly adjusting the price to reflect the discount. You end up with the sale price, the amount a customer would pay after the discount is applied.

Mastering Rounding Decimals

When working with currency, precise rounding is crucial to ensure prices are accurately presented, especially in business contexts. After calculating the discount amount, if you end up with a long decimal, it needs to be rounded to two decimal places. This is standard for prices because it aligns with the representation of cents in dollars.

• For example: $4.4985 becomes $4.50
• Look at the third decimal place: if it's 5 or more, round up the second decimal. Otherwise, keep it as is.

Rounding helps maintain neat and clear financial transactions, making it easier for both sellers and buyers to understand the final costs involved.