Question

At Bruno's Video World, the regular price for a DVD is d dollars. How many DVDs can be purchased for x dollars when the DVDs are on sale at 20% off the regular price?

• A. 4/5x
• B. 5/4x
• C. 4/5d
• D. 4x/5d
• E. 5x/4d

Hint:

A 20% discount means you pay 80% of the original price. 80% is 80/100 or 4/5. So the sale price is simply (4/5)d. The number of items is always Total Money / Price per Item.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This is a word problem involving percentages. We first need to calculate the sale price of a single DVD and then determine how many of them can be bought with a given amount of money.

Step 2: Detailed Explanation:
First, find the sale price of one DVD.
The regular price is \( d \) dollars.
The discount is 20% of the regular price.
\[ \text{Discount amount} = 20% \text{ of } d = 0.20 \times d = 0.2d \] The sale price is the regular price minus the discount amount.
\[ \text{Sale Price} = d - 0.2d = 0.8d \] We can also express this price as a fraction:
\[ 0.8d = \frac{8}{10}d = \frac{4}{5}d \] Next, find how many DVDs can be purchased for \( x \) dollars.
The number of items that can be purchased is the total amount of money available divided by the price per item.
\[ \text{Number of DVDs} = \frac{\text{Total money}}{\text{Sale Price per DVD}} \] \[ \text{Number of DVDs} = \frac{x}{\frac{4}{5}d} \] To divide by a fraction, we multiply by its reciprocal.
\[ \text{Number of DVDs} = x \times \frac{5}{4d} = \frac{5x}{4d} \]

Step 3: Final Answer:
The number of DVDs that can be purchased is \(\frac{5x}{4d}\).