Problema Solution
tents hold 2,3,5,6, or 12 people. how many combinations are possible to sleep 30 if all tents are fully occupied and exactly one 12 person tent is being used?
Answer provided by our tutors
let
a = the number of tents that hold 2 people
b = the number of tents that hold 3 people
c = the number of tents that hold 5 people
d = the number of tents that hold 6 people
2a + 3b + 5c + 6d + 12 = 30
2a + 3b + 5c + 6d = 30 - 12
2a + 3b + 5c + 6d = 18
if we assume that all the possible tents are occupied that is: a>0, b>0, c>0, d>0
we know that
2*1 + 3*1 + 5*1 + 6*1 = 16
thus the only possible combination is:
2*2 + 3*1 + 5*1 + 6*1 = 18
2 tents that can hold 2 people each
1 tent that can hold 3 people
1 tent that can hold 5 people
1 tent that can hold 6 people