Problem 64 - Introductory Algebra for College Students

Question

Formulas frequently appear in the business world. For example, the cost, \(C,\) of an item (the price paid by a retailer) plus the markup, \(M,\) on that item (the retailer's profit) equals the selling price, \(S,\) of the item. The formula is $$C+M=S$$ Use the formula. The selling price of a television is \(\$ 650 .\) If the cost to the retailer for the television is \(\$ 520,\) find the markup.

Step-by-Step Solution

Answer

The markup on the television is \$130.

Step 1: Identify given values

The exercise gives us the selling price \(S = \$ 650\) and the cost to the retailer \(C = \$ 520\). We are asked to find the markup \(M\).

Step 2: Substitute known values into the equation

Using the formula \(C + M = S\), substitute \(C = \$ 520\) and \(S = \$ 650\), which changes the equation to \(520 + M = 650\).

Step 3: Solve for M

To find the markup \(M\), we need to isolate \(M\) on one side of the equation. We can do this by subtracting \(520\) from both sides of the equation. This gives us: \(M = 650 - 520\).

Step 4: Calculate the value of M

After the subtraction, we get \(M = \$ 130\).

Step 5: Confirm the result

The markup, or the retailer's profit on the television, is \$130.

Key Concepts

Understanding Equations in Business Mathematics

Equations are a fundamental part of introductory algebra and are crucial for solving business math problems. They express relationships between different values using mathematical symbols. In our example, the formula \( C + M = S \) demonstrates the relationship between cost (\( C \)), markup (\( M \)), and selling price (\( S \)).

This equation shows how the selling price is split between cost and profit. By rearranging it, you can solve for any unknown value if you have the other two. This is handy in business where understanding costs and profits is important for decision making. Here, knowing how to manipulate and solve equations helps businesses to price products correctly, ensuring they make profits.

Problem-Solving Techniques

Problem-solving involves using mathematical techniques to find solutions. In the exercise, we followed logical steps to find the markup (\( M \)) from the given values.

Here's a simple approach to tackling such problems:

• Identify what you need to find.
• Gather and understand all given information.
• Substitute known values into the relevant equation.
• Isolate the variable you need to solve for.
• Perform the necessary calculations.

In this case, we substituted \( C = \\(520 \) and \( S = \\)650 \) into \( C + M = S \) and then solved for \( M \) by subtraction. This method allows for easy problem-solving in both business and everyday math scenarios.

Role of Business Mathematics

Business mathematics is about applying math concepts to solve business-related problems. It encompasses everything from pricing strategies to financial analysis.

Let's consider how mathematics is used in pricing strategies. Businesses use formulas to determine the right selling price that covers costs and ensures a good profit margin. For example, knowing the cost and required profit helps in guiding how much a product should be marked up, as demonstrated by the formula \( C + M = S \).

This understanding allows businesses to stay competitive and profitable by making informed financial decisions. Thus, a strong foundation in business math is essential for anyone pursuing a career in the business sector.