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Chapter 6: Problem 9

Lu Chan wants to leave a tip of \(18 \%\) on a dinner check of \(\$ 52.48\) About how much should he leave?

Short Answer

Expert verified
Lu Chan should leave a tip of about $9.45.

Step by step solution

01

Understand the Problem

We have a dinner check for $52.48, and Lu Chan wants to leave an 18% tip. The question asks us to find out how much the tip should be.
02

Convert Percent to Decimal

To find 18% of a number, convert the percentage to a decimal by dividing by 100. Therefore, 18% becomes 0.18.
03

Multiply to Find the Tip Amount

Multiply the total dinner check amount ($52.48) by the decimal (0.18) to find the tip: \( 52.48 \times 0.18 \).
04

Calculate the Result

Perform the multiplication: \( 52.48 \times 0.18 = 9.4464 \).
05

Round to the Nearest Cent

Round 9.4464 to the nearest cent. Since the third decimal is 4, we round down to 9.45.

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Key Concepts

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

Understanding Decimal Conversion
Decimal conversion is the process of changing a percentage into a decimal form, which is essential for various mathematical calculations, especially with percentages. When you have a percentage, such as 18%, you are dealing with a part per hundred. To convert it into a decimal, you simply divide by 100. This step transforms 18% into 0.18. This decimal form is what you use in calculations, like determining a tip.
  • Divide the percentage by 100
  • Example: 18% becomes 0.18
  • This is the decimal used in multiplications
Converting percentages to decimals is straightforward but foundational for working with percentages in mathematical operations.
Effective Multiplication
Multiplication plays a crucial role when you're looking to determine values like a tip from a percentage. Once you have your percentage converted into a decimal, the next step is to multiply it by the total amount of interest. In this case, the total dinner check, $52.48, is your amount of interest.
  • Step 1: Convert percentage to a decimal (0.18)
  • Step 2: Multiply by the total amount (e.g., $52.48)
  • Step 3: Calculate the total (e.g., $52.48 脳 0.18 = $9.4464)
Understanding how to multiply correctly is crucial, as it directly affects the outcome, such as knowing how much tip to leave.
The Basics of Rounding
Rounding is essential for everyday math problems to make numerical figures easier to understand and work with. Once you perform a multiplication that results in a long decimal, like 9.4464, rounding comes into play. Rounding ensures that you present figures in a more manageable form. In currency, rounding to the nearest cent is commonplace. Rounding involves looking at the digit beyond your desired decimal place and adjusting the last digit.
  • Identify the digit you鈥檙e rounding to (e.g., nearest cent)
  • Look at the next digit to decide (4 means you round down)
  • Adjust the number accordingly (9.45 in this example)
By rounding 9.4464 to 9.45, you effectively determine the tip Lu Chan should leave.
Mastering Problem Solving
Problem solving is an overarching skill combining all the smaller steps into a coherent solution. For example, in calculating a tip, you have several interconnected steps. First, understand what the problem is asking: how much tip should Lu Chan leave on a $52.48 check if he wants to tip 18%? Then, follow a structured approach:
  • Clarify the problem and what is needed
  • Convert the given percentage into a decimal
  • Use multiplication to find the precise tip amount
  • Round the calculated tip to the nearest cent for practicality
This structured sequence helps break down complex issues into manageable parts, guiding you towards accurate and reliable answers.

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Most popular questions from this chapter

Solve each problem using the percent equation. 17.6 is \(133 \frac{1}{3} \%\) of what number?

Solve each equation. Check your solution. $$5.6=80 w$$

Find each sum or difference. Write in simplest form. $$ \frac{25}{8}+\frac{7}{8} $$

Complete each sentence. 78 inches \(=\quad\) feet

Express each percent as a fraction or mixed number in simplest form and as a decimal. (lesson \(6-5\) ) \(56 \%\)
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