Problem 155 - Elementary Algebra

Question

Leaving a Tip At the campus coffee cart, a medium coffee costs \$1.65. MaryAnne brings \(\$ 2.00\) with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave?

Step-by-Step Solution

Answer

MaryAnne leaves a tip of approximately 21.2%.

Step 1: Calculate the change MaryAnne leaves as a tip

MaryAnne pays \(2.00 for a medium coffee that costs \)1.65. To find the change left as a tip, subtract the cost of the coffee from the amount paid: Tip amount = \$ 2.00 - \$ 1.65 = \$ 0.35

Step 2: Calculate the percent tip based on the coffee cost

To find the percentage tip, divide the tip amount by the cost of the coffee and multiply by 100: Percent Tip = \( \frac{\$0.35}{\$1.65} \times 100 \) Percent Tip = \( \frac{0.35}{1.65} \times 100 \approx 21.2 \% \)

Key Concepts

Calculating Tips

When you leave a tip, you are giving an extra amount of money to show appreciation for the service. Tips are usually calculated as a percentage of the total bill.
To calculate the tip, follow these steps:

• First, determine the amount you wish to tip.
• Next, decide the percentage you want to give. Common tip percentages are 10%, 15%, and 20%.
• Finally, multiply the total bill amount by the tip percentage (expressed as a decimal). For example, to tip 15% on a bill of \(\text{\textdollar}50\), you would multiply \(\text{\textdollar}50\) by 0.15, giving you \(\text{\textdollar}7.50\).

This way, you can always ensure you're leaving an appropriate tip based on the service you received.
In this exercise, MaryAnne chose to leave her change (\text{\textdollar}0.35) as a tip, and we calculated this amount as a percentage of the coffee cost.

Subtraction

Subtraction is one of the basic arithmetic operations. It allows you to find out how much one number is less than another.
In this context, subtraction helps us find out how much money MaryAnne has left to tip after buying her coffee.
Here's how you do it:

• Identify the numbers you are working with. MaryAnne has \(\text{\textdollar}2.00\) and spends \(\text{\textdollar}1.65\) on coffee.
• Subtract the smaller number (cost of coffee) from the larger number (money she had). In this case, it is \(\text{\textdollar}2.00 - \text{\textdollar}1.65\).
• The result is the amount left: \(\text{\textdollar}2.00 - \text{\textdollar}1.65 = \text{\textdollar}0.35\).

Subtraction is straightforward but crucial for determining remaining amounts and balances in everyday scenarios.

Division

Division is another fundamental arithmetic operation. It allows you to distribute a number into equal parts.
For calculating percentages, division is essential. It helps in figuring out what part of a whole the number represents.
Here's how you use division in the tip calculation:

• Identify the tip amount (\text{\textdollar}0.35) and the cost of the coffee (\text{\textdollar}1.65).
• Divide the tip amount by the coffee cost: \(\frac{\text{\textdollar}0.35}{\text{\textdollar}1.65} = 0.212\).
• To get the percentage, multiply this result by 100: \(0.212 \times 100 \rightarrow 21.2\text{\textpercentage}\).

Following these steps, you can understand that MaryAnne left a 21.2% tip, showcasing the importance of division in calculating percentages effectively.