Problem 27 - Thinking Mathematically

Question

A storeowner ordered 25 calculators that cost \(\$ 30\) each. The storeowner can sell each calculator for \(\$ 35\). The storeowner sold 22 calculators to customers. He had to return 3 calculators and pay a \(\$ 2\) charge for each returned calculator. Find the storeowner's profit.

Step-by-Step Solution

Answer

The storeowner's profit is \$14.

Step 1: Calculate Total Cost of Calculators

The total cost of the calculators can be calculated by multiplying the number of calculators ordered by the cost of each calculator. Therefore, the total cost equals \(25 \times \$30 = \$750\).

Step 2: Calculate Total Income from Selling Calculators

The total income from selling calculators can be computed by multiplying the number of calculators sold by the selling price of each calculator. In this scenario, total income from selling calculators equals \(22 \times \$35 = \$770\).

Step 3: Calculate Returned Calculators’ Charges

The total charges for the returned calculators equals the number of returned calculators multiplied by the charge for each returned calculator. Hence, total charges for returned calculators equals \(3 \times \$2 = \$6\).

Step 4: Determine Total Profit

Finally, the total profit is obtained by subtracting the total cost and charges from total income. So the profit equals \( \$770 - \$750 - \$6 = \$14 \).

Key Concepts

Profit Calculation

Calculating profit is fundamental when running a business, especially in retail. It determines how much a business earns after covering its costs. To calculate profit, we use the formula:

• Profit = Total Income - Total Costs - Other Expenses

In the given example, the storeowner ordered and sold calculators, and had to manage costs associated with the purchase and return. By applying the profit formula:

• Total Income was derived from selling the calculators.
• Total Costs came from buying them.
• Other Expenses included the charges for returning some calculators.

By subtracting the total costs and added expenses (from returns) from the income, we find the net earnings or profit, which is the end goal in a business transaction. In this specific problem, the storeowner made a profit of \(\$14\) after considering all relevant financial elements.

Cost and Income Analysis

Understanding cost and income analysis helps in assessing the financial health of a business. Costs are the expenses incurred in acquiring or producing goods, while income is what is earned from selling those goods.

• Total Cost: In this scenario, the total cost was calculated based on the number of calculators purchased (25 calculators) at a specific cost per item (\\(30 each), resulting in \(25 \times \\)30 = \\(750\).
• Total Income: Likewise, income was derived by selling 22 calculators at a selling price of \\)35 each, totaling \(22 \times \\(35 = \\)770\).

It's crucial to distinguish between these terms, as they form the foundation of any financial analysis. Further expense considerations like the returns of products add a layer of complexity to the cost side, emphasizing the importance of comprehensive financial planning.

Step-by-Step Solutions

Implementing a step-by-step method for solving mathematical problems is a reliable approach to avoid errors and improve clarity. Here's how it was applied to determine the storeowner's profit in this exercise: 1. **Total Cost Calculation:** Here, the cost of purchasing all calculators was calculated using multiplication. 2. **Total Income Calculation:** The next step involved computing the income earned from sold calculators, again using multiplication. 3. **Returning Costs Analysis:** Any additional costs, such as charges for returned items, were also considered separately. 4. **Final Profit Computation:** The final step was to put these figures together - subtracting the costs and return charges from the total income to find the profit. This methodical approach ensures each part of the problem is handled systematically, reducing mistakes and enhancing understanding. Through clear steps, such problems become manageable, ensuring students and business owners don't overlook any financial details.