A local transit company sells a monthly pass for $95 that allows an unlimited number of trips of any length.

Question

A local transit company sells a monthly pass for $95 that allows an unlimited number of trips of any length. Tickets for individual trips cost $1.50, $2.50, or $3.50, depending on the length of the trip. What is the minimum number of trips per month for which a monthly pass could cost less than purchasing individual tickets for trips?

Accepted Answer

The correct answer is 28. The minimum number of individual trips for which the cost of the monthly pass is less than the cost of individual tickets can be found by assuming the maximum cost of the individual tickets, $3.50. If n tickets costing $3.50 each are purchased in one month, the inequality 95 < 3.50 n represents this situation. Dividing both sides of the inequality by 3.50 yields 27.14 < n , which is equivalent to n > 27.14. Since only a whole number of tickets can be purchased, it follows that 28 is the minimum number of trips.

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