Real Life Example of Linear Equation in Two Variables

In many real-life situations, we encounter linear equations in two variables. One such example is the problem of calculating the total cost of a taxi ride based on the distance traveled and the initial fare. Let's consider the following scenario:

Problem:
A taxi charges $2.50 as an initial fare and an additional $1.20 per mile. How much will it cost to travel a certain distance?

Variables:
Let's assign variables to the given information:
- Distance traveled: Let's denote this variable as 'd'.
- Total cost of the taxi ride: Let's denote this variable as 'C'.

Linear Equation:
To determine the total cost 'C' of the taxi ride based on the distance 'd' traveled, we can set up the following linear equation:
C = 2.50 + 1.20d

Explanation:
- The constant term '2.50' represents the initial fare charged by the taxi. It is independent of the distance traveled.
- The term '1.20d' represents the additional cost per mile covered. It is directly proportional to the distance traveled.
- By adding the initial fare and the additional cost per mile, we can determine the total cost of the taxi ride.

Example:
Suppose a person travels a distance of 10 miles. To calculate the total cost of the taxi ride, we substitute 'd = 10' into the linear equation:
C = 2.50 + 1.20(10)
C = 2.50 + 12
C = 14.50

Therefore, the total cost of the taxi ride for a 10-mile distance would be $14.50.

Conclusion:
Linear equations in two variables are commonly encountered in various real-life scenarios. In the given example, we used a linear equation to calculate the total cost of a taxi ride based on the distance traveled and the initial fare. By understanding and applying such equations, we can solve practical problems and make informed decisions.