Problem 47 - Algebra 1

Question

The charge for a cab ride is S11.50, and you give a 20\% tip. Using the model, find the total cost of the cab ride. Describe what the variable a represents. Model \(2: a\) is \(120 \%\) of \(\$ 11.50 .\)

Step-by-Step Solution

Answer

The total cost of the cab ride (represented by 'a') is $13.80. 'a' represents the total cost of the cab ride, which includes the initial charge and the tip.

Step 1: Understand the Model

In the provided model 'a is 120% of $11.50,' 'a' is the total cost of the cab ride including the tip. As the tip is 20%, this makes the total cost 120% of the amount $11.50.

Step 2: Calculate the Total Cost

From the model, calculate 120% of $11.50. This can be done by multiplying 120/100 (which is the decimal equivalent of 120%) by 11.50. The result will yield the total cost of the cab ride.

Step 3: Describe the Variable

'a' represents the total cost of the cab ride, including the set fare of $11.50 and the 20% tip which equates to 120% of the set fare. Thus 'a' is the sum you pay after the ride.

Key Concepts

Calculating Cost

When calculating the total cost of a service, like a cab ride, it's important to understand all contributing factors, including the base price and any additional charges. In our example, the base cost of the cab ride is $11.50. However, we must also consider the tip to determine the total cost.
The cost can be broken into:

• Base fare: $11.50
• Tip: 20% of base fare

By adding these components, we reveal the complete cost. To find this, we convert percentages to decimals and multiply. This way, we calculate what 20% of $11.50 adds to this base cost. This final number represents the entire expense of your cab ride.

Algebraic Model

In the world of mathematics, understanding how to use algebraic models helps in simplifying and solving problems. In this exercise, the model states that 'a is 120% of $11.50.' Here, 'a' is a variable used to represent the total cost, including the cab fare and tip.
To use this model effectively, it involves transforming the percentage into a workable form:

• Convert 120% to a decimal by dividing it by 100, giving us 1.20.
• Multiply 1.20 by the base fare of $11.50.

This results in the total cost that 'a' represents. By following this approach, we break down the problem into simpler steps, easily calculating the aftermath of adding a percentage increase to a base amount.

Tip Calculation

Calculating a tip is a common real-world application of percentages. Tips are often calculated as a percentage of the original amount. In this scenario, the tip is set at 20%.
Here's how to calculate it:

• Identify the original amount, which is $11.50 in this case.
• Determine the percentage of the tip - here, it's 20%.
• Convert this percentage into a decimal (20% becomes 0.20).
• Multiply 0.20 by the original amount of $11.50 to find the tip amount.

Once you have the tip amount, you simply add it to the base fare to arrive at the total payment needed. This method is straightforward and ensures you’re providing the right amount based on the standard tipping percentage.