Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To determine the correct formula for calculating the fare for [tex]\( x \)[/tex] kilometers traveled by an auto-rickshaw, we can break down the problem step by step.
1. Initial Cost for the First Kilometer:
- The fare for the first [tex]\( 1 \)[/tex] kilometer (km) is fixed at Rs. [tex]\( 10 \)[/tex].
2. Cost for Additional Distance:
- For every kilometer beyond the first kilometer, the fare is Rs. [tex]\( 4.50 \)[/tex] per kilometer.
Based on these rules, let's consider each answer choice and check if it aligns with the given fare structure:
A. [tex]\( 4.5(x-1) + 10 \)[/tex]:
This formula suggests:
- After the first kilometer, only the additional kilometers are charged at the rate of Rs. [tex]\( 4.50 \)[/tex] per km.
- So, for [tex]\( x \)[/tex] kilometers, if [tex]\( x \leq 1 \)[/tex], the fare is Rs. [tex]\( 10 \)[/tex].
- If [tex]\( x > 1 \)[/tex], the fare would be Rs. [tex]\( 10 \)[/tex] (first km) [tex]\( + 4.5(x-1) \)[/tex] (remaining kilometers).
This seems correct because it correctly adds the base charge and charges the remaining distance separately.
B. [tex]\( 10(x-1) + 4.5 \)[/tex]:
This formula suggests:
- For [tex]\( x - 1 \)[/tex] kilometers, the fare is Rs. [tex]\( 10 \)[/tex] per kilometer.
- Adding Rs. [tex]\( 4.5 \)[/tex] as a flat fee.
This formula incorrectly applies the Rs. [tex]\( 10 \)[/tex] rate to the kilometers beyond the first km, and the additional Rs. [tex]\( 4.5 \)[/tex] doesn't fit the given structure.
C. [tex]\( 4.5x + 10 \)[/tex]:
This formula suggests:
- Rs. [tex]\( 4.5 \)[/tex] per km for [tex]\( x \)[/tex] kilometers.
- Adding Rs. [tex]\( 10 \)[/tex] as an additional flat fee.
This formula does not correctly account for the specific rate for the first km being different from the subsequent kilometers.
D. [tex]\( 10x + 4.5 \)[/tex]:
This formula suggests:
- A flat rate of Rs. [tex]\( 10 \)[/tex] per kilometer for [tex]\( x \)[/tex] kilometers.
- Adding Rs. [tex]\( 4.5 \)[/tex] as an additional fee.
This formula also does not correctly account for the different rates for the first kilometer and the subsequent kilometers.
Conclusion:
The correct general rule to calculate the fare for [tex]\( x \)[/tex] kilometers traveled is:
A. [tex]\( 4.5(x-1) + 10 \)[/tex]
1. Initial Cost for the First Kilometer:
- The fare for the first [tex]\( 1 \)[/tex] kilometer (km) is fixed at Rs. [tex]\( 10 \)[/tex].
2. Cost for Additional Distance:
- For every kilometer beyond the first kilometer, the fare is Rs. [tex]\( 4.50 \)[/tex] per kilometer.
Based on these rules, let's consider each answer choice and check if it aligns with the given fare structure:
A. [tex]\( 4.5(x-1) + 10 \)[/tex]:
This formula suggests:
- After the first kilometer, only the additional kilometers are charged at the rate of Rs. [tex]\( 4.50 \)[/tex] per km.
- So, for [tex]\( x \)[/tex] kilometers, if [tex]\( x \leq 1 \)[/tex], the fare is Rs. [tex]\( 10 \)[/tex].
- If [tex]\( x > 1 \)[/tex], the fare would be Rs. [tex]\( 10 \)[/tex] (first km) [tex]\( + 4.5(x-1) \)[/tex] (remaining kilometers).
This seems correct because it correctly adds the base charge and charges the remaining distance separately.
B. [tex]\( 10(x-1) + 4.5 \)[/tex]:
This formula suggests:
- For [tex]\( x - 1 \)[/tex] kilometers, the fare is Rs. [tex]\( 10 \)[/tex] per kilometer.
- Adding Rs. [tex]\( 4.5 \)[/tex] as a flat fee.
This formula incorrectly applies the Rs. [tex]\( 10 \)[/tex] rate to the kilometers beyond the first km, and the additional Rs. [tex]\( 4.5 \)[/tex] doesn't fit the given structure.
C. [tex]\( 4.5x + 10 \)[/tex]:
This formula suggests:
- Rs. [tex]\( 4.5 \)[/tex] per km for [tex]\( x \)[/tex] kilometers.
- Adding Rs. [tex]\( 10 \)[/tex] as an additional flat fee.
This formula does not correctly account for the specific rate for the first km being different from the subsequent kilometers.
D. [tex]\( 10x + 4.5 \)[/tex]:
This formula suggests:
- A flat rate of Rs. [tex]\( 10 \)[/tex] per kilometer for [tex]\( x \)[/tex] kilometers.
- Adding Rs. [tex]\( 4.5 \)[/tex] as an additional fee.
This formula also does not correctly account for the different rates for the first kilometer and the subsequent kilometers.
Conclusion:
The correct general rule to calculate the fare for [tex]\( x \)[/tex] kilometers traveled is:
A. [tex]\( 4.5(x-1) + 10 \)[/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
