Problem 14 - Algebra A Combined Function

Question

A retirement dinner for two is \(\$ 65.40\) including tax. Find the total cost if a \(20 \%\) tip is added to the cost.

Step-by-Step Solution

Answer

The total cost with a 20% tip is $78.48.

Step 1: Calculate the Tip Amount

To find the tip amount, calculate 20% of the original cost. Multiply the cost by 0.20: \[ \\text{Tip} = 65.40 \times 0.20 = 13.08 \\] This means the tip amount is \$13.08.

Step 2: Calculate the Total Cost

Add the tip to the original cost to find the total amount to be paid. \[ \\text{Total Cost} = 65.40 + 13.08 = 78.48 \\] So, the total cost with tip is \$78.48.

Key Concepts

Tip Calculation

Calculating a tip involves using one of the fundamental aspects of percentages in math. It's a way to show gratitude for service in many parts of the world. When you want to tip, you simply calculate a percentage of the total bill.
A common tip percentage is 20%. To find this, convert the percentage to a decimal by dividing by 100, which gives you 0.20. Then, multiply this by the total amount of the bill. In our example, the original cost for the meal including tax was $65.40. Thus, the calculation for the tip is as follows:

• Convert the percentage to a decimal: 20% becomes 0.20
• Multiply the bill by this decimal: $65.40 × 0.20

This calculation gives us $13.08, which represents the tip amount. It's always a good practice to double-check your multiplication to ensure you have the correct tip amount.

Cost Calculation

After calculating the tip, the next step involves adding this amount to the original cost to find the total payment. This step ensures you understand how much you are paying altogether, including the gratitude for the service.
To do this, simply add the amount of the tip to the original bill. In our scenario, the original bill was $65.40 and we found the tip to be $13.08. The calculation is simple:

• Add the original cost and the tip: $65.40 + $13.08

The result is $78.48, which is the total amount you will pay. This includes the original cost plus the extra gratitude shown to the server.

Arithmetic Operations

Arithmetic operations are basic math skills that include addition, subtraction, multiplication, and division. These operations are used daily in situations like our dining bill example.
When calculating tips and total costs, you typically use multiplication and addition. In our example:

• Multiplication was used to calculate the 20% tip.
• Addition was applied to sum the tip and the original cost to get the total payment.

Being comfortable with these operations helps make everyday financial decisions easier and more accurate. It's beneficial to practice them regularly so you can handle similar calculations swiftly in real-life scenarios. Remember, the ability to quickly double-check your work can also save you from simple errors.