Problem 10 - Algebra 1

Question

What percent was the server’s tip if the customer left \(1.75 for a \)12.50 meal?

Step-by-Step Solution

Answer

The server's tip was 14% of the total cost of the meal.

Step 1: Identify the tip and the total cost of the meal

The tip is \(1.75. The total cost of the meal is \)12.50.

Step 2: Set up the percentage equation

A percentage is always a portion of 100, so to find the percentage of the tip, divide the tip by the total cost of the meal and multiply by 100. The equation is: \((1.75 / 12.50) \times 100\).

Step 3: Calculate the percentage

Perform the operations to find the answer. \((1.75 / 12.50) \times 100 = 14\%\).

Key Concepts

Tip Calculation

Understanding how to calculate a tip is a valuable skill for many situations, such as dining out. A tip is typically a percentage of the total bill given to the service staff as a gratuity for their service. Here's how you can calculate it:

• First, identify the amount of the tip and the total bill.
• Next, divide the tip amount by the total bill to find the decimal representation of the percentage.
• Finally, convert this decimal to a percentage by multiplying it by 100.

For example, if you left a $1.75 tip on a $12.50 meal, divide $1.75 by $12.50 to get the decimal 0.14. When you multiply 0.14 by 100, the tip is 14% of the total bill.

This method can help you calculate tips quickly and accurately in any situation.

Ratio and Proportion

Understanding the concept of ratios and proportions is crucial when solving percentage problems. A ratio is a way to compare two quantities by dividing them. For example, in the problem above, the ratio of the tip to the total meal cost is \( \frac{1.75}{12.50} \). This ratio shows the relationship between the tip and the meal cost.

A proportion, on the other hand, is an equation that states that two ratios are equivalent. In tip calculations, converting this ratio into a percentage creates a proportion. By setting up the equation \( \frac{1.75}{12.50} = \frac{x}{100} \), you can solve for \( x \), which gives you the percentage of the tip related to the meal cost.

• Calculate the ratio of the tip to the total bill.
• Set this ratio equal to the desired proportion (out of 100).
• Solve the equation using basic arithmetic operations.

This approach simplifies understanding the proportional relationship in percentage calculations.

Basic Arithmetic Operations

Basic arithmetic operations are essential in tip and percentage calculations. The main operations are addition, subtraction, multiplication, and division. Here’s how they apply:

• Addition: Typically used when calculating the total of a bill.
• Subtraction: Not directly applicable to tips but useful in refunds or adjustments.
• Multiplication: Converting a decimal to a percentage involves multiplying by 100.
• Division: Used to find the ratio between the tip and total cost — divide the tip amount by the meal cost.

In the step-by-step solution of the given problem, you use division to determine the tip's ratio to the meal. Then, you utilize multiplication to convert this ratio into a percentage.

Mastering these operations is crucial as they allow for efficient and error-free computation of tips and percentages.