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The taxi fare in a town is ₹ 10 for the first kilometer and ₹ 6 per km for the subsequent distance. Taking the distance as [tex] x \, \text{km}[/tex] and the total fare as [tex] z[/tex], write a linear equation for this information. What will be the total fare for 15 km?

Sagot :

GinnyAnswer
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.
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