Home Hardware paid $123 for a particular type of drill. Expenses are 12% of selling price and the required profit is 22% of selling price. Round ALL answers to the nearest cent if applicable.

1) What is the regular selling price?

$


2) What is the break-even selling price?

$


3) During an inventory sale, the drill was marked down 22% on the regular selling price. What is the sale price?

$


4) What is the operating profit or loss during the inventory sale (use a negative sign (-) for a loss)?

$

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To solve these problems, we will set up equations based on the given information and solve for the desired quantities.

### 1. Regular Selling Price

Let $ S $ be the regular selling price.

Expenses are 12% of the selling price, which is $ 0.12S $.

The required profit is 22% of the selling price, which is $ 0.22S $.

The cost price (what Home Hardware paid) is $123.

The equation can be set up as:
\[ \text{Cost Price} = \text{Selling Price} - \text{Expenses} - \text{Profit} \]

\[ 123 = S - 0.12S - 0.22S \]

Combining the terms:
\[ 123 = S(1 - 0.12 - 0.22) \]

\[ 123 = S(0.66) \]

Solving for $ S $:
\[ S = \frac{123}{0.66} \]

\[ S = 186.36 \]

So, the regular selling price is **$186.36**.

### 2. Break-Even Selling Price

The break-even selling price is the price at which there is no profit or loss. This means the selling price only needs to cover the expenses and cost price.

Let $ B $ be the break-even selling price.

The equation is:
\[ \text{Cost Price} + \text{Expenses} = \text{Break-Even Selling Price} \]

\[ 123 + 0.12B = B \]

Rearranging the equation:
\[ 123 = B - 0.12B \]

\[ 123 = B(1 - 0.12) \]

\[ 123 = B(0.88) \]

Solving for $ B $:
\[ B = \frac{123}{0.88} \]

\[ B = 139.77 \]

So, the break-even selling price is **$139.77**.

### 3. Sale Price During Inventory Sale

During the inventory sale, the drill is marked down by 22% of the regular selling price.

\[ \text{Sale Price} = S - 0.22S \]

\[ \text{Sale Price} = 186.36 - 0.22 \times 186.36 \]

\[ \text{Sale Price} = 186.36 - 41.00 \]

\[ \text{Sale Price} = 145.36 \]

So, the sale price during the inventory sale is **$145.36**.

### 4. Operating Profit or Loss During Inventory Sale

Operating profit or loss is calculated as:

\[ \text{Operating Profit/Loss} = \text{Sale Price} - \text{Cost Price} - \text{Expenses} \]

\[ \text{Expenses} = 0.12 \times \text{Sale Price} = 0.12 \times 145.36 = 17.44 \]

\[ \text{Operating Profit/Loss} = 145.36 - 123 - 17.44 \]

\[ \text{Operating Profit/Loss} = 145.36 - 140.44 \]

\[ \text{Operating Profit/Loss} = 4.92 \]

So, the operating profit during the inventory sale is **$4.92**.

Would you like more details or have any questions?

Here are 8 relative questions to further expand on this topic:

1. What would the selling price be if expenses were 15% instead of 12%?
2. How does an increase in the cost price affect the selling price and profit margin?
3. What is the impact of reducing the required profit margin to 18% on the selling price?
4. How would a different markdown percentage (e.g., 30%) during the inventory sale affect the sale price?
5. What is the formula to calculate the break-even price if the cost price and expense percentage are known?
6. How does changing the expense percentage affect the break-even price?
7. What would be the new profit or loss if the sale price was marked down by 25% instead of 22%?
8. How does the sale price compare to the cost price if there is no profit margin included?

**Tip:** Always double-check your calculations for rounding errors to ensure accuracy in financial problem-solving.

Learn how to calculate the regular selling price, break-even selling price, sale price during inventory sale, and operating profit or loss using a Home Hardware drill example. Includes step-by-step solutions and rounding to the nearest cent.

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