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Chapter 8: Problem 65

Make Sense? In Exercises 65-68, determine whether each statement makes sense or does not make sense, and explain your reasoning. i have \(\$ 100\) and my restaurant bill comes to \(\$ 80\), which is not enough to leave a \(20 \%\) tip.

Short Answer

Expert verified
The statement does not make sense as there would be $4 remaining even after paying the bill and the 20% tip.

Step by step solution

01

Calculate the Tip

Firstly, calculate the 20% tip on the restaurant bill. The bill is $80. The tip would therefore be \(0.20 * 80 = \$16\).
02

Calculate Remaining Amount

Now, deduct the amount of the bill along with the tip from the total amount available. This would be \(100 - 80 - 16 = \$4\).
03

Analyze the Statement

As a result, there is still $4 remaining after paying the bill and the 20% tip. Thus, the statement 'I have $100 and my restaurant bill comes to $80, which is not enough to leave a 20% tip.' does not make sense.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Percentage Calculation
Percentage calculation is a fundamental aspect of arithmetic and is essential for everyday situations like figuring out discounts, taxes, and tips. To calculate a percentage, you multiply the base amount by the percentage rate expressed as a fraction or a decimal. For example, in the original problem, a 20% tip on an $80 restaurant bill is calculated by multiplying 80 by 0.20. The result, $16, represents 20% of the original bill.

This process can be broken down into simple steps:
  • First, convert the percentage into a decimal by dividing by 100. For instance, 20% becomes 0.20.
  • Next, multiply the base amount (in this case, the restaurant bill of $80) by the decimal (0.20). The result is $16, which is the amount of tip to be added.
Practicing percentage calculations in different scenarios helps build confidence and speed in financial decision-making.
The Art of Problem-Solving in Real Life Scenarios
Problem-solving is more than just mathematical calculations; it involves critical thinking and evaluating information to reach a conclusion. The original problem required the analysis of a financial scenario where you had $100 and faced expenses totaling $96 ($80 for the bill and $16 for the tip). Understanding whether leaving the tip was feasible required breaking down the budget and considering all parts of the transaction.

Effective problem-solving steps include:
  • Identify the problem clearly. Here, it was determining whether $100 would cover both the bill and the tip.
  • Break down the problem into manageable parts 鈥� calculate each expense separately.
  • Use logical reasoning to analyze your findings. In this case, calculating the remaining balance after expenses.
By practicing detailed evaluation and calculation, you can handle unexpected situations more confidently and efficiently.
Building Financial Literacy
Financial literacy is about understanding how to manage money effectively, which includes skills like budgeting, saving, and understanding expenses. In the given problem, recognizing how much money remains after covering basic expenses like bills and tips is a critical exercise in financial management.

To improve financial literacy, consider these helpful approaches:
  • Regularly practice calculations that involve real-life expenses, like tips, taxes, and discounts, to become comfortable with managing money.
  • Create a budget plan to track your income and expenses. Knowing where your money goes helps in making informed financial choices.
  • Engage in scenarios that test your ability to plan and adjust your finances. Just like in the problem, check if your funds cover necessary expenses and prepare for surprises.
Being financially literate empowers you to make sound decisions and manage financial challenges with ease.

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