A Boston-based band plays some gigs throughout New England,

Question

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. [Hint: find the “break even point” – where both rental plans cost the same.]

Answer 1

g = # of gigs

Cost of Renting Van per Gig = 120g ($120 * g)

Cost of Renting Van for the Year = 3800  ($3000 + $800)

 

Set the two costs equal to each other to get that 120g = 3800, and g = 31.6666667

 

So at 31 gigs, it is still cheaper to rent the van each trip.... you have only spent $3,720 (less than $3800).

However, once you are at 32 gigs, you have spent $3840 (more than $3800)

 

The question asks what is the minimum number of trips to save money by renting the van for the entire year... it is asking when is it cheaper to rent the van for the year... and that stops at 31 gigs.  Once the band hits 32 gigs, you are no longer saving money.