Solving with Linear Equations

This problem can be solved by setting up and solving a system of two linear equations with two variables.

1. Define the Variables

• Let B be the fare from city A to city B.
• Let C be the fare from city A to city C.

2. Formulate the Equations

We can translate the two statements in the problem into mathematical equations:

• "Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77"
  Equation (1): 2B + 3C = 77
• "three tickets from city A to B and two tickets from city A to C cost Rs. 73"
  Equation (2): 3B + 2C = 73

3. Solve the System of Equations

A simple way to solve this is to first add the two equations together, and then subtract one from the other.

Adding the equations:

(2B + 3C) + (3B + 2C) = 77 + 73

5B + 5C = 150

Dividing by 5, we get: B + C = 30 (Equation 3)

Subtracting equation (1) from (2):

(3B + 2C) - (2B + 3C) = 73 - 77

B - C = -4 (Equation 4)

Now we solve the new, simpler system:

B + C = 30
B - C = -4

Adding these two equations gives:

2B = 26 → B = 13

Substitute B = 13 into Equation 3:

13 + C = 30 → C = 17

Conclusion

The fare for city B is Rs. 13 and the fare for city C is Rs. 17.