Problem 66 - Elementary Algebra

Question

A restaurant bill is \(\$ 65\). If the tip is \(20 \%\) of the bill, find the total cost of the meal including tip.

Step-by-Step Solution

Answer

The total cost of the meal including tip is \(\text{\textdollar} 78\).

Step 1 - Find the Tip

To find the amount of the tip, multiply the bill amount by the tip percentage. The bill amount is \(\text{\textdollar} 65\) and the tip percentage is \(20\%\). So, \(\text{Tip} = \text{\textdollar} 65 \times \frac{20}{100} = \text{\textdollar} 65 \times 0.20 = \text{\textdollar} 13\).

Step 2 - Calculate the Total Cost

To find the total cost of the meal including the tip, add the tip amount to the original bill amount. The bill amount is \(\text{\textdollar} 65\) and the tip amount is \(\text{\textdollar} 13\). So, \(\text{Total Cost} = \text{\textdollar} 65 + \text{\textdollar} 13 = \text{\textdollar} 78\).

Key Concepts

Percentage Calculations

Understanding how to calculate percentages is a vital math skill that we use in various situations. In our exercise, we needed to find 20% of the total bill amount to determine the tip.
To calculate a percentage, we can use the following method:

• Convert the percentage into a decimal by dividing by 100. For example, 20% becomes 0.20 when divided by 100.
• Multiply this decimal by the total bill amount. In our case, that means multiplying 0.20 by 65.
• Perform the multiplication: \( 0.20 \times 65 = 13 \). This tells us the tip amount in dollars.

Remembering these simple steps will make calculating percentages much easier.
Whether you are dealing with tips, discounts, or interest rates, percentage calculations are everywhere.

Basic Arithmetic

In our exercise, we used basic arithmetic to find the total cost of the meal. Basic arithmetic includes the basic operations of addition, subtraction, multiplication, and division.

• We first used multiplication to find the tip amount: \( 65 \times 0.20 = 13 \).
• Next, we used addition to calculate the total cost by adding the original bill and the tip together: \( 65 + 13 = 78 \).

Understanding and being comfortable with these basic operations is crucial, as they form the foundation for more complex math problems.
Practice these simple operations frequently to build a strong mathematical base. Simple problems like this help reinforce these basic arithmetic skills.

Real-Life Math Applications

Math is not just about abstract ideas; it's something we use every day in real-life situations. Calculating the total cost of a meal with a tip is a perfect example.
In a real-world setting, knowing how to calculate a tip quickly and accurately can save you from under or overpaying.

• Group bills might need percentage calculations to figure out individual shares or tips.
• Understanding this concept ensures fairness and clarity in social situations.

By practicing these real-life math applications, you'll find managing finances easier, whether dining out, shopping, or planning a budget.
Real-life applications make math practical and applicable, turning complex concepts into useful everyday skills.