Question

The entire family chartered a boat for the day for $840. Unfortunately, one couple had severe colds and had to cancel, so the remaining members had to chip in another $35 each. How many people were there originally?

Answer 1

let original number of people be n
so original cost per person = 840/n

final number of people = n-2
final cost per person = 840/n + 35

then (n-2)((840/n) + 35) = 840

expanding, multiplying each term by n, then reducing to lowest terms gave me
n^2 - 2n - 48 = 0
(n-8)(n+6)
so n=8 or n=-6
(can't have negative number of people)

n = 8

originally there were 8 people

check: for 8 people cost pp = 840/8 = 105
new cost pp = 105 + 35 = 140
for 6 people : 6(140) = 840
Yeah!