A bus company has 4000 passengers daily, each paying a fare of $2. For each $0.15 increase, the company estimates that it will lose 40 passengers. If the company needs to take in $10,450 per day to stay in business, what fare should be charged?
Damon answered this same question back in 2009
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To determine the fare that should be charged, we need to find the fare amount that will generate a revenue of $10,450 while taking into account the estimated passenger loss for each fare increase.
Let's start by assuming the fare charged is $2. From the given information, we know that there are 4000 passengers and each pays $2 fare. Therefore, the total revenue generated per day would be:
Total revenue = Number of passengers * Fare amount
Total revenue = 4000 * $2
Total revenue = $8000
However, the company needs to generate a revenue of $10,450 per day to stay in business, so we need to account for the remaining amount:
Remaining revenue needed = Required revenue - Total revenue
Remaining revenue needed = $10,450 - $8000
Remaining revenue needed = $2450
Now, we have to consider the estimated passenger loss for each $0.15 increase in fare. It is given that for each $0.15 increase, the company estimates a loss of 40 passengers. We can use this information to determine the fare increase required to generate the remaining revenue needed:
Fare increase = Remaining revenue needed / (Estimated passenger loss * $0.15)
Fare increase = $2450 / (40 * $0.15)
Fare increase = $2450 / $6
Fare increase ≈ $408.33
Finally, we can calculate the fare that should be charged by adding the fare increase to the initial fare:
Fare = Initial fare + Fare increase
Fare = $2 + $408.33
Fare ≈ $410.33
Therefore, the fare that should be charged is approximately $410.33 in order to generate a revenue of $10,450 and cover the estimated passenger loss due to fare increase.