# At \$18 per ticket, how many people must buy tickets so that the trip need not be cancelled?A group has chartered a bus to Niagara Falls. The driver costs \$100, the bus costs \$500, and trip...

At \$18 per ticket, how many people must buy tickets so that the trip need not be cancelled?

A group has chartered a bus to Niagara Falls. The driver costs \$100, the bus costs \$500, and trip insurance( purchased the day of the trip) will cost \$75. The driver’s fee is nonrefundable, but the bus may be cancelled a week in advance at a charge of only \$50.

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

There are no given minimum requirements nor notice period by which time the bus and driver must be booked. Each of the costs (including the insurance) are fixed, regardless of the number of passengers. Therefore, to cover the expenses:

\$100 + \$500 + \$75 = \$675

take the amount to be paid and divide by the amount of each ticket

\$675 / \$18 = 37,50

As people cannot be split into halves, 38 people would need to buy tickets.

A consideration would be that, if  there are not enough people - at least one week before - as long as three people have bought tickets, there will be enough to cover the \$50 cancellation fee.

Obviously, if there are almost enough people and, despite advertising the trip, there is no more interest shown, consideration should be given to increasing the cost of the ticket. Use a similar calculation to calculate the new price if you have say, only 30 people:

\$675/ 30 = \$ 22,50

Accordingly, at \$18 per ticket, with no other considerations, 38 people must buy tickets.