Problem 43 - Elementary Algebra

Question

Translate each sentence to a mathematical statement and then simplify. The revenue for a local photographer for the month is \(\$ 1,200\). His costs include a studio rental of \(\$ 600\), props costing \(\$ 105,\) materials fees of \(\$ 135,\) and a make-up artist who charges \(\$ 120 .\) What is his total profit for the month?

Step-by-Step Solution

Answer

The photographer's total profit for the month is $240.

Step 1: Identify the Revenue

The revenue is the total amount of money earned by the photographer during the month. From the problem statement, the revenue is given as $1,200.

Step 2: Calculate Total Costs

List all costs incurred by the photographer:- Studio Rental: \(600- Props: \)105- Materials Fees: \(135- Make-up Artist: \)120Sum these costs to get the total expenses:\( \text{Total Costs} = 600 + 105 + 135 + 120 \)

Step 3: Perform the Addition

Calculate the sum:\( \text{Total Costs} = 600 + 105 + 135 + 120 = 960 \)

Step 4: Calculate the Profit

The profit is determined by subtracting the total costs from the revenue. Use the formula:\( \text{Profit} = \text{Revenue} - \text{Total Costs} \)

Step 5: Subtract Costs from Revenue

Substitute the given values:\( \text{Profit} = 1,200 - 960 = 240 \)

Step 6: Conclude the Profit

The profit for the photographer for the month is $240.

Key Concepts

Revenue

Revenue represents the total amount of money a business or individual earns over a specified period without considering any costs or expenses. In this case, the local photographer's revenue for the entire month is \(\$ 1,200\). This value indicates how well the business is performing in terms of generating income.

• Revenue is crucial because it's the starting point in calculating profit.
• It simply refers to all income before deducting any costs or expenses.
• Helping to measure how much money is flowing into the business over time.

Understanding revenue helps in evaluating if future investments are necessary and how changes might affect overall business profitability."

Total Costs

Calculating total costs involves summing up all expenses associated with running a business or completing a project within a given period. It represents the money spent to produce and deliver services. In the photographer's scenario:

• Studio rental costs \(\\( 600\).
• Props cost \(\\) 105\).
• Material fees are \(\\( 135\).
• The make-up artist charges \(\\) 120\).

To determine total costs, you add these expenses: \[ \\( 600 + \\) 105 + \\( 135 + \\) 120 = \$ 960 \].This total signifies how much money has been utilized to maintain the operations for the month. It’s vital to keep these costs manageable, ensuring they don’t exceed the revenue. Calculating and understanding total costs are steps in managing a successful business, as it helps identify areas where spending can be reduced.

Expense Calculation

Expense calculation is critical for maintaining financial health and involves totaling up all costs incurred within a specific timeframe. This process aids in understanding cash flow and ensuring that the income is consistently higher than expenses to achieve profitability.In our exercise, you calculate the exact expenses (like rent and fees) and total them as follows, \[ \\( 960= \\) 600\, +\, \\( 105\, +\, \\) 135\, +\, \$ 120 \]. This provides clarity on the financial outgoings.

• Tracking expenditures helps in budgeting and forecasting.
• Expense calculation keeps you informed about cash flow.
• Monitoring these figures regularly ensures the financial sustainability of the business.

By knowing all outgoing costs, a business can make informed decisions and implement strategies to improve efficiency and cut down unnecessary expenses.

Mathematical Statement Translation

Translating word problems into mathematical statements involves understanding the problem thoroughly and then expressing it using equations and numerical expressions. This skill is vital for solving real-world problems efficiently.In the given problem, here's how you translate and solve for the profit:- Identify revenue (given as \(\\(\, 1200\))- Deduct total costs (calculated as \(\\)\, 960\)) from the revenue to find profit.You setup the equation as \[ \text{Profit} = \text{Revenue} - \text{Total Costs} \]This translates to \[ \text{Profit} = \\(\, 1200\, -\, \\)\, 960 = \$\, 240 \].Recognizing key components in the problem narrative and translating them into the appropriate mathematical form allows you to compute accurate results. This empowers you to tackle various mathematical problems effectively, improving both problem-solving skills and mathematical comprehension.