Problem 63 - Introductory and Intermediate Algebra for College Students 4th

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 $$C+M=S$$ The selling price of a computer is \(\$ 1850 .\) If the markup on the computer is \(\$ 150,\) find the cost to the retailer for the computer.

Step-by-Step Solution

Answer

The cost to the retailer for the computer is \$1700.

Step 1: Understand and Rearrange the Formula

You have the formula \(C + M = S\). To find \(C\), you need to rearrange this formula. This gives you \(C = S - M\).

Step 2: Substitute the Given Values

Now, replace \(S\) with \(\$1850\) and \(M\) with \(\$150\) in the rearranged formula. So it becomes \(C = \$1850 - \$150\).

Step 3: Calculate the Cost

Perform the subtraction to find the cost. Therefore, \(C = \$1700\).

Key Concepts

Business Mathematics

Business mathematics plays a vital role in the functioning of businesses. It's the application of mathematical methods and formulas in real business scenarios.
This field helps in analyzing and solving problems related to finance, investment, production, and more.

• Business mathematics enables businesses to handle their operations efficiently.
• It aids in making informed decisions by providing quantitative insights.

By leveraging mathematical formulas, such as the one detailed in our exercise, businesses can determine key financial figures like cost, markup, and selling prices.
Such calculations are essential for proper financial management and ensuring profitability.

Markup and Selling Price

Understanding markup and selling price is crucial for any retail business.
Markup is the additional amount added to the cost price of a product, comprising the retailer's profit.

• Markup ensures that retailers cover their expenses and earn a profit.
• Selling price is the sum of the cost of the item and the markup.

The markup can be calculated as: \[ M = S - C \] Where:
- \(M\) is the markup
- \(S\) is the selling price
- \(C\) is the cost price
By understanding these concepts, a business can strategically price its products to remain competitive and profitable.

Cost Calculation

Accurate cost calculation is a fundamental aspect of running a successful business.
It involves determining the total expenses that a retailer incurs to procure a product. Here, we calculate cost using the simple formula: \[ C = S - M \] This formula helps in identifying the cost price when the selling price and markup are known.

• The selling price is the final price at which a product is sold to consumers.
• Markup represents the profit margin added by the retailer.

By accurately calculating costs, businesses can set appropriate selling prices and ensure profitable operations. This comprehensive understanding safeguards against potential losses and enhances financial planning.