SOLUTION: A ferryboat operator charges a fee for crossing a river. You have the choice between paying a fare of $2 per trip or to pay $10 for a pass that allows you to receive a 25% discount

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Question 296198: A ferryboat operator charges a fee for crossing a river. You have the choice between paying a fare of $2 per trip or to pay $10 for a pass that allows you to receive a 25% discount from the regular price for each crossing. What is the least number of times that you must cross the river so that you would pay less by buying the pass than by paying the full fare each time you cross?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A ferryboat operator charges a fee for crossing a river. You have the choice between paying a fare of $2 per trip or to pay $10 for a pass that allows you to receive a 25% discount from the regular price for each crossing. What is the least number of times that you must cross the river so that you would pay less by buying the pass than by paying the full fare each time you cross?
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Flat fee cost: F(x) = 2x where x is number of crossings
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Variable fee cost: V(x) = 10 + 0.75(2x) where x is number of crossings
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Solve 10 + (3/4)(2x) < 2x
10 + (3/2)x < 2x
10 < (1/2)x
x > 20
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Ans to Question: 21 crossings
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Cheers,
Stan H.