Question

After paying a \(6 \frac{1}{4} \%\) sales tax, Jerome paid \(\$ 135.20\) for a set of Blu-ray discs that listed for \(\$ 149.70\) but was on sale at a discount. To the nearest whole percent, what was the discount on the set before sales tax? A. \(6 \%\) B. \(7 \%\) C. \(14 \%\) D. \(15 \%\)

Short answer

The discount was approximately \ 15\text{ \%}. The correct answer is D.

Step-by-step solution

Identify the Actual Price Paid Before Tax

Jerome paid \$ 135.20\ after a sales tax of \6 \frac{1}{4} \%\. First, subtract the sales tax from the total price. Let \x\ be the price before sales tax.\[ x + 0.0625x = 135.20 \] Combine like terms: \[ 1.0625x = 135.20 \] Solve for \x\: \[ x = \frac{135.20}{1.0625} \] \[ x \approx \ 127.25 \] Therefore, the price before tax was approximately \$ 127.25\.

Calculate the Discount

The original listed price was \$ 149.70\ and the price before tax was \$ 127.25\. Now, find the discount amount by subtracting the price before tax from the listed price: \[ \text{Discount amount} = 149.70 - 127.25 \] \[ \text{Discount amount} = 22.45 \]

Find the Discount Percentage

Now calculate the discount percentage given the discount amount and the original price. Use the following formula: \[ \text{Discount percentage} = \frac{\text{Discount amount}}{\text{Original price}} \times 100 \] Substitute the given values: \[ \text{Discount percentage} = \frac{22.45}{149.70} \times 100 \] Calculate the percentage: \[ \text{Discount percentage} \approx \ 15 \% \]

Key concepts

percentage calculation

Percentage calculations are fundamental in understanding many GED math problems. A percentage represents a part of a whole and is often used to express how one quantity relates to another. For example, if you have a discount of 15% on an item, it means the discount is 15 parts out of 100 of the original price. Understanding how to compute percentages is essential for solving problems involving discounts, sales tax, and price adjustments. You often use formulas like this:
\( \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \).
This formula helps you to find the portion represented by a percentage of a total. For instance, in our example, Jerome bought Blu-ray discs and we had to find the discount percentage.

sales tax

Sales tax is an additional amount charged on the price of goods. It is a percentage of the item's price and adds to the total cost. To compute the sales tax amount, use the formula: \( \text{Sales Tax} = \text{Price} \times \text{Sales Tax Rate} \).
In our exercise, Jerome paid \(6 \frac{1}{4} \%\) in sales tax. First, convert the fraction to a decimal form: \(6.25\% = 0.0625 \).
If Jerome’s final cost after tax was \(135.20, we can find the pre-tax price by setting up an equation: \( x + 0.0625x = 135.20 \). Breaking that down, \(1.0625x = 135.20 \). Solving for \( x \), the pre-tax price, gives us \( x \) approximately \)127.25.

discount calculation

Discount calculation is essential for determining the savings on purchases. Discounts are often offered as percentages off the original price. To find the discount amount, subtract the sale price from the original price. Then, to find the percentage discount, use the formula:
\( \text{Discount Percentage} = \frac{\text{Discount Amount}}{\text{Original Price}} \times 100 \).
In Jerome’s case, the original price was \(149.70, and the price before tax was approximately \)127.25. Subtract these to get the discount amount: \(149.70 - 127.25 = 22.45 \).
To find the discount percentage: \( \frac{22.45}{149.70} \times 100 \) yields approximately 15%. So, the discount offered to Jerome was around 15%.

price adjustment

Price adjustment involves altering the initial price based on factors like discounts, sales tax, or other fees. Understanding how and when to apply these adjustments is crucial for solving real-world math problems. For example:

• If there’s a discount, subtract the discount amount from the original price to find the new price.
• If sales tax is added, first calculate the tax and then add it to the pre-tax price.

In Jerome’s case, the price was adjusted twice: first for a discount and second for sales tax. Initially, the price of \(149.70 was adjusted by a discount of 15%, bringing it down to approximately \)127.25. Afterwards, sales tax of 6.25% was added to this discounted price, resulting in the final amount Jerome paid, which was $135.20. Understanding these steps ensures accurate calculations.