Word Problem

[bdelaughter]

A tour group wishes to rent a bus. There is a fixed fee for renting a bus plus a fee of $5 per person. Suppose a tour group has enough people to rent a bus at a cost of $15 per person. However, the group is able to recruit 6 more people to the tour bringing the cost down to $11.25 per person to rent the bus. How many people are in the group?

 

[arthur ohlsten]

let the number of people be P
total cost of the bus=15P
let the fixed cost for the bus be B
total cost = B+5P
15P=B+5P
B=10P we will use this later

if P increases by 6 then total cost = 11.25[P+6]
total cost = B+5[P+6]
set total cost = total cost
11.25[P+6]=B+5[P+6]
11.25P+67.5=B+5P+30
6.25P+37.5=B but B=10P
6.25P+37.5=10P
37.5=3.75P
P=10 answer

please check for errors
Arthur