Answer :
Final Answer:
Benjamin would need to take the bus more than [tex]\( \frac{F}{P - 2} \)[/tex] times for the Frequent Flyer Deal to be cheaper than the pay-as-you-go option.
Explanation:
To determine how many times Benjamin would need to take the bus to make the Frequent Flyer Deal cheaper than the pay-as-you-go option, we need to compare the total cost of each option over a certain number of bus trips.
Let's denote:
- [tex]\( F \)[/tex] as the cost of the Frequent Flyer Deal.
- [tex]\( P \)[/tex] as the cost per bus trip for the pay-as-you-go option.
- [tex]\( n \)[/tex] as the number of bus trips.
The total cost of the Frequent Flyer Deal after taking [tex]\( n \)[/tex] bus trips is [tex]\( F + 2n \)[/tex]
The total cost of the pay-as-you-go option after taking [tex]\( n \)[/tex] bus trips is [tex]\( n \times P \)[/tex]
We want to find the value of [tex]\( n \)[/tex] for which the total cost of the Frequent Flyer Deal is cheaper than the pay-as-you-go option:
[tex]\[ F + 2n < n \times P \][/tex]
Solving for [tex]\( n \)[/tex], we get:
[tex]\[ n > \frac{F}{P - 2} \][/tex]
Therefore, Benjamin would need to take the bus more than [tex]\( \frac{F}{P - 2} \)[/tex] times for the Frequent Flyer Deal to be cheaper than the pay-as-you-go option.
