The Bellinger store charger $30 for each computer - game DVD. The store charges this price keeping a profit margin of 20% During Christmas, to increase sales, the store offers a discount of 10% on the cost of the DVD. By what amount is the price of a DVD during Christmas less than the normal price offered by the store ?

Options

A. 5
B. 6
C. 7.5
D. 8.4

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Determine the Selling Price (SP) and Profit Margin
The Bellinger store charges $30 for each computer game DVD, which is the selling price (SP). The profit margin is 20%.

**Hint:** Remember that the profit margin is a percentage of the cost price (CP).

### Step 2: Set Up the Equation for Cost Price (CP)
Let the cost price (CP) be represented as \( x \). The profit is 20% of the cost price, which can be expressed as \( 0.2x \).

The selling price is given by the formula:
\[ SP = CP + \text{Profit} \]
Substituting the known values, we have:
\[ 30 = x + 0.2x \]

**Hint:** Combine the terms on the right side of the equation.

### Step 3: Simplify the Equation
Combining \( x \) and \( 0.2x \):
\[ 30 = 1.2x \]

**Hint:** To isolate \( x \), divide both sides by 1.2.

### Step 4: Solve for Cost Price (CP)
Now, we solve for \( x \):
\[ x = \frac{30}{1.2} = 25 \]
So, the cost price of the DVD is $25.

**Hint:** Make sure to check your division to ensure accuracy.

### Step 5: Calculate the Discount Offered During Christmas
The store offers a discount of 10% on the cost price during Christmas. Therefore, the discount can be calculated as:
\[ \text{Discount} = 0.1 \times 25 = 2.5 \]

**Hint:** Remember that the discount is a percentage of the cost price, not the selling price.

### Step 6: Determine the Selling Price During Christmas
The selling price during Christmas is the cost price minus the discount:
\[ \text{Selling Price during Christmas} = 25 - 2.5 = 22.5 \]

**Hint:** Ensure you are subtracting the discount from the cost price, not the selling price.

### Step 7: Find the Difference Between Normal Price and Christmas Price
To find out by how much the price during Christmas is less than the normal price, we subtract the Christmas selling price from the normal selling price:
\[ \text{Difference} = 30 - 22.5 = 7.5 \]

**Hint:** This step involves simple subtraction to find the difference in prices.

### Conclusion
The price of a DVD during Christmas is $7.5 less than the normal price offered by the store.

**Final Answer:** $7.5