Sure! Let's write a linear equation for the given taxi fare information and then calculate the total fare for a 15 km journey.
### Taxi Fare Structure
1. The fare for the first kilometer is ₹ 10.
2. The fare for each subsequent kilometer is ₹ 6.
Given:
- Distance traveled [tex]\( x \)[/tex] km
- Total fare [tex]\( z \)[/tex]
The linear equation for fare calculation can be written as:
[tex]\[ z = 10 + 6(x - 1) \][/tex]
Here, [tex]\( 10 \)[/tex] is the fare for the first kilometer, and [tex]\( 6(x - 1) \)[/tex] is the fare for the subsequent kilometers.
### Calculating the Total Fare for 15 km
1. Distance traveled: [tex]\( x = 15 \)[/tex] km
2. Plug this value into the equation:
[tex]\[ z = 10 + 6(15 - 1) \][/tex]
3. Simplify the equation step-by-step:
- Calculate the subsequent distance: [tex]\( 15 - 1 = 14 \)[/tex] km
- Calculate the fare for the subsequent distance: [tex]\( 6 \times 14 = 84 \)[/tex]
- Add the fare for the first kilometer: [tex]\( 10 + 84 = 94 \)[/tex]
### Final Result
The total fare for a 15 km journey is ₹ 94.
