Prisha buys sculptures from Toronto and sells them in her studio in Vancouver. She purchases the sculptures from a gallery in Toronto for $3,000, less discounts of 25% and 10%. Her overhead expenses are 9.5% on the cost and she would like to make a profit of 45% on the cost of the sculptures. Calculate the following:

**a.** Regular selling price of the sculptures.

To calculate the regular selling price of the sculptures, we need to follow these steps:

1. **Determine the net purchase price after discounts**.
2. **Calculate the overhead expenses**.
3. **Determine the desired profit**.
4. **Calculate the regular selling price**.

Let's go through each step in detail.

### Step 1: Determine the Net Purchase Price After Discounts

The original price of the sculptures is $3,000. The gallery offers two successive discounts of 25% and 10%. 

First, apply the 25% discount:
\[ \text{Price after first discount} = 3000 \times (1 - 0.25) \]
\[ \text{Price after first discount} = 3000 \times 0.75 \]
\[ \text{Price after first discount} = 2250 \]

Next, apply the 10% discount on the reduced price:
\[ \text{Net purchase price} = 2250 \times (1 - 0.10) \]
\[ \text{Net purchase price} = 2250 \times 0.90 \]
\[ \text{Net purchase price} = 2025 \]

### Step 2: Calculate the Overhead Expenses

The overhead expenses are 9.5% of the net purchase price:
\[ \text{Overhead expenses} = 2025 \times 0.095 \]
\[ \text{Overhead expenses} = 192.375 \]

### Step 3: Determine the Desired Profit

Prisha wants to make a profit of 45% on the cost of the sculptures (net purchase price):
\[ \text{Desired profit} = 2025 \times 0.45 \]
\[ \text{Desired profit} = 911.25 \]

### Step 4: Calculate the Regular Selling Price

The regular selling price is the sum of the net purchase price, overhead expenses, and desired profit:
\[ \text{Regular selling price} = \text{Net purchase price} + \text{Overhead expenses} + \text{Desired profit} \]
\[ \text{Regular selling price} = 2025 + 192.375 + 911.25 \]
\[ \text{Regular selling price} = 3128.625 \]

Thus, the regular selling price of the sculptures is **$3128.63**.

Do you want any more details or have any questions?

Here are 5 numbered questions for you to ask:
1. How do I calculate the markup percentage based on cost?
2. Can you explain how to solve exponential growth problems?
3. What is the formula for compound interest and how is it derived?
4. How do I find the integral of a trigonometric function?
5. What are the key differences between mean, median, and mode?

Tip: When dealing with multiple discounts, apply each discount sequentially to get the correct final price.

Learn how to calculate the regular selling price of sculptures purchased with discounts and including overhead expenses and desired profit margin. This problem involves applying successive discounts, calculating overhead costs as a percentage of purchase price, and determining profit margin based on cost. Useful for understanding pricing strategies and business calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation