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A short class with Sarah and her students. The other ways are under More.
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Today, we have a real-world application of linear equations. Let's consider a scenario where a taxi charges a base fare plus a rate per kilometer. Does anyone want to suggest how we might start solving this?
We could start by identifying the fixed and variable costs.
Great! That's right. The fixed cost, or the base fare, is $5. Now, what about the cost per kilometer?
It's $2 for each kilometer driven.
Exactly! So if we represent the number of kilometers with 'x', what equation can we form?
The equation would be C = 2x + 5.
You got it! Now, if we want to calculate the cost for a ride of 10 kilometers, what do we do next?
Now that we have our equation, let's calculate the cost for a 10 km ride. What substitution should we make?
We should substitute x with 10 in the equation C = 2x + 5.
Correct! Let’s perform the substitution. What do we get?
C = 2(10) + 5 = 20 + 5 = 25.
So the total cost for the ride is $25. This is a perfect example of how linear equations can be used in real-life situations. Any questions about this?
For every kilometer, two bucks you'll pay, plus five on the meter to make your day, hey!
Imagine you're taking a taxi to your party. The driver smiles and says it's $5 just to start, and $2 for each laugh you share as you drive, keeping it in your heart!
For taxi costs, think of '2km + 5$' or use '2 x K + 5'.
Use the acronym TFC for Taxi Fare Calculation: T = Total cost, F = Fixed cost, C = Cost per km.
Term
Equation for Taxi Fare
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Term
Cost Calculation
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An equation that makes a straight line when graphed, with each term being a constant or a product of a constant and a single variable.
A cost that varies depending on the quantity of usage, such as distance traveled in a taxi ride.
A cost that does not change with the level of output; for example, a base fare on a taxi ride.
This section illustrates how to form and solve a linear equation using a real-world scenario.
The section focuses on applying linear equations to real-life situations, specifically highlighting a taxi fare problem. It provides the formulation of the equation and a detailed calculation to find the total cost of a ride.
In this section, we explore the application of linear equations to a practical scenario involving taxi fares. Here, we need to develop a linear equation based on the problem statement, which states that a taxi charges a fixed rate plus a variable rate depending on distance traveled.
The cost, denoted as C, can be represented as:
C = 2x + 5
Where x is the number of kilometers traveled.
For a ride of 10 km:
Through this example, students learn not only to write a linear equation from a word problem but also to perform calculations using the equation. This skill is essential in solving real-world problems using algebra.