Problem 55 - Algebra 1

Question

A pest control company had a profit of \(\$ 3,514.65\) in April, a profit of \(\$ 5,674.25\) in May, a loss of \(\$ 8,992.88\) in June, and a loss of \(\$ 1,207.03\) in July. Did the company make a profit during the 4 -month period? Explain.

Step-by-Step Solution

Answer

To determine the overall profit (or loss), we sum up all the values: \$3,514.65 + \$5,674.25 - \$8,992.88 - \$1,207.03 = -\$1,011.01. Since the result is negative, the company did not make a profit during these four months.

Step 1: Identify the profits and losses

It is clear that the company made a profit of \$3,514.65 in April and \$5,674.25 in May. For June, the company incurred a loss of \$8,992.88. In July there was a further loss of \$1,207.03.

Step 2: Convert the losses into negative values

In terms of numbers, a loss indicates a negative value. Hence, the loss of \$8,992.88 in June will be written as -\$8,992.88 and the loss of \$1,207.03 in July will be noted as -\$1,207.03.

Step 3: Sum up all values

To determine if the company made an overall profit during these four months, sum up all the values by adding: \$3,514.65 + \$5,674.25 + (-\$8,992.88) + (-\$1,207.03).

Step 4: Evaluate the result

If the result of the sum is positive, then the company made an overall profit. If the result is negative or zero, the company did not make a profit.

Key Concepts

Arithmetic Operations

When working with profit and loss calculations, understanding arithmetic operations is crucial. The essential operation here is addition, but when dealing with losses, subtraction gets involved. We consider the following steps for the arithmetic operations needed:

• Identify different types of values: profits are positive numbers, whereas losses are negative numbers.
• Combine these values by performing addition and subtraction as indicated by their signs.
• For example, if a company has profits of \(\\(3,514.65\) in April and \(\\)5,674.25\) in May, we add these numbers.
• Next, the losses for June and July are \(-\\(8,992.88\) and \(-\\)1,207.03\), which will be subtracted when summed up due to their negative signs.
• Evaluate the total to make the final determination of profit or loss.

It’s important to carefully handle negative numbers in this context, as misinterpretation can lead to incorrect results.

Financial Literacy

Financial literacy is the understanding and application of various financial skills, including accounting for profits and losses. It's crucial for businesses, like our pest control company, to track these numbers accurately to assess financial health. Here's why financial literacy matters:

• Tracking Profits and Losses: Knowing how to determine whether your business is making a profit or suffering a loss over a specific period is pivotal.
• Decision Making: Accurate information about the company's financial standing helps in making informed decisions, such as where to cut costs or how to boost revenue.
• Budgeting: By understanding these numbers, businesses can allocate their resources more efficiently.

Financial literacy empowers entities to navigate economic fluctuations and helps in planning for future growth, ensuring sustainability and success.

Negative Numbers

Negative numbers often represent losses in financial statements. They’re crucial for depicting the financial performance of businesses:

• Representation: In accounting, expenses or losses are usually represented with a negative sign. This signifies an outflow of resources or reduction in financial standing.
• Calculations: Properly utilizing negative numbers in calculations helps accurately reflect the net result, whether it is a profit or a loss.
• Interpretation: A negative result in a financial equation such as adding profits and subtracting losses implies that total losses outweigh the gains, leading to an overall loss.

In the pest control example, converting losses into negative numbers was key in computing the overall financial outcome. An understanding of how to properly work with negative values is essential to correctly evaluating and interpreting financial data.