Problem 18 - Prealgebra

Question

BUSINESS An entrepreneur owns two restaurants and is reviewing their earnings for first and second quarters. The first restaurant earned \(\$ 17,821\) in the first quarter and \(\$ 18,331\) in the second. The second restaurant earned \(\$ 8112\) in the first quarter and \(\$ 9920\) in the second. Which restaurant increased their earnings by the greatest percent? By what percent did that restaurant's earnings increase?

Step-by-Step Solution

Answer

Restaurant 2 increased their earnings by the greatest percent, approximately 22.28%.

Step 1: Calculate the increase in earnings for each restaurant

First, we need to determine how much each restaurant's earnings increased from the first quarter to the second. For Restaurant 1, subtract the first quarter earnings from the second quarter earnings: \[ 18331 - 17821 = 510 \] For Restaurant 2, subtract the first quarter earnings from the second quarter earnings: \[ 9920 - 8112 = 1808 \]

Step 2: Calculate the percent increase for Restaurant 1

Calculate the percent increase for Restaurant 1 by dividing the increase by the first quarter's earnings and multiplying by 100:\[ \frac{510}{17821} \times 100 \approx 2.86\% \]

Step 3: Calculate the percent increase for Restaurant 2

Calculate the percent increase for Restaurant 2 by dividing the increase by the first quarter's earnings and multiplying by 100:\[ \frac{1808}{8112} \times 100 \approx 22.28\% \]

Step 4: Compare the percent increases

Finally, compare the percent increases calculated in the previous steps: Restaurant 1 had an increase of approximately 2.86%, and Restaurant 2 had an increase of approximately 22.28%. Therefore, Restaurant 2 had the greater percent increase in earnings.

Key Concepts

Understanding Percentage Increase

When we talk about percentage increase, we identify how much a certain quantity has grown in comparison to its original amount. It's a way of expressing growth as a fraction of the initial value. This concept is pivotal in understanding various situations, from business earnings to financial investments.

To calculate percentage increase, you would follow these steps:

• First, determine the increase by subtracting the original value from the new value.
• Next, divide this increase by the original amount to find the proportion of growth compared to the starting point.
• Finally, convert this proportion to a percentage by multiplying it by 100.

This entire process helps in providing a clear picture of how much something has grown in a relative sense rather than just its absolute increase.

The Role of Financial Literacy

Financial literacy is the ability to understand and use financial skills, such as budgeting and investing. In the context of percentage increase, financial literacy can help people and businesses wisely evaluate their financial decisions.

For instance, knowing how to calculate and compare the percentage increases of different income streams can empower an entrepreneur to make informed decisions about where to focus their resources or cut back. Moreover, understanding these concepts can help in predicting future trends, managing risks, and optimizing profits.

Mastering Step-by-Step Problem Solving

In solving math problems, especially those involving real-world applications such as finance, a step-by-step approach can often provide clarity and prevent errors. By breaking down a problem into manageable parts, we build a structured way of thinking.

The process can be broken down into key stages:

• Read and understand the problem statements carefully.
• Identify what is being asked and the necessary information needed to solve it.
• Develop a plan by deciding which mathematical operations and formulas should be used.
• Execute the plan by performing the calculations needed.
• Review the results to ensure they make sense within the context of the problem.

By following these steps, individuals can approach complex scenarios with greater confidence, especially when dealing with intricate financial data.