Math Question Help

Question

A Boston-based band plays some gigs throughout New England, and is trying to decide whether it makes more sense to rent a van for a day each time it gets a gig outside the Boston Area, or if it should rent a van for the entire year. Renting a van to travel to a gig costs $120 for the rental, which includes insurance. Renting a van for the year costs $3000 for the van, and another $800 for insurance. What is the minimum number of trips that the band needs to make during the upcoming year in order for it to save money by renting a van for the entire year? Your answer should be an integer. 

Answer 1

Let x be the number of trips.

 

If they rent the van each time, the cost will be 120x.

 

The total cost to rent the van for the year will be 3800.

 

So you want to find the minimum value for x so that 3800 < 120 x

 

Let's solve the inequality:

 

3800 < 120 x

3800 / 120 < x

31.6666 < x

 

Since they don't do fractional gigs, you have to find the smallest integer x that's greater than 31.666, and that's 32.