Problem 13 - Algebra A Combined Function

Question

A birthday celebration meal is \(\$ 40.50\) including tax. Find the total cost if a \(15 \%\) tip is added to the cost.

Step-by-Step Solution

Answer

The total cost with a 15% tip is $46.58.

Step 1: Identifying Given Information

We know that the cost of the meal including tax is given as $40.50. We need to find the total cost when a 15% tip is added to this amount.

Step 2: Calculating the Tip Amount

The tip is calculated as 15% of the total meal cost. To find this, multiply the cost of the meal by 0.15: \\[ 40.50 \times 0.15 = 6.075 \]

Step 3: Rounding the Tip Amount

It is common to round monetary amounts to two decimal places. So, we round $6.075 to $6.08.

Step 4: Adding the Tip to the Meal Cost

Add the rounded tip amount to the original cost of the meal to find the total cost. \\[ 40.50 + 6.08 = 46.58 \]

Step 5: Verification

Verify the calculation by checking each step for accuracy and ensuring that rounding does not significantly alter the result.

Key Concepts

Understanding Tip Calculation

When you're dining out, leaving a tip is a common custom to show appreciation for good service. To calculate a tip, you first need to determine the percentage you want to leave. In many places, a tip of 15% to 20% is typical.
Here’s a simple approach:

• Start by determining the initial amount, which in this case is the meal cost including tax, $40.50.
• Next, calculate the tip by multiplying the meal cost by the tip percentage expressed as a decimal. For a 15% tip, you convert this to 0.15.
• So, the calculation is: \( 40.50 \times 0.15 = 6.075 \). This amount is the tip before any rounding.

Understanding tips can help in quickly making calculations, whether it’s during a meal out or for any service-related gratitude, making sure both the service provider and the customer have a positive experience.

Rounding in Arithmetic

Rounding is an essential mathematical technique often used in financial calculations. It's crucial when you need to simplify a number while maintaining its value as closely as possible.
Let’s look at how rounding works in our example:

• The calculated tip was $6.075. In financial contexts, we round to two decimal places, as they represent cents.
• To round $6.075, look at the number in the third decimal place (5). According to rounding rules, if this digit is 5 or higher, you round up.
• This means $6.075 becomes $6.08 when rounded. This ensures clarity in billing and avoids disputes over penny differences.

Rounding helps provide clear and concise financial statements and is a skill beneficial beyond just paying bills or leaving tips.

Real-Life Math Applications

Mathematics is not just for the classroom; it plays a significant role in everyday life. One practical application is in calculating bills and tips.
Here’s why understanding this is beneficial:

• It enhances numeracy skills, allowing quick mental math computation.
• Helps in budgeting and financial planning by managing expenses and gratuities effectively.
• Encourages the right amount of tipping, keeping good customer relationships, and the goodwill of service employees.

This exercise in calculating a tip on a meal demonstrates the everyday use of percentages and rounding, showcasing how mathematical concepts are woven into daily routines and decision-making processes.