Orange Computers is breaking up its conference attendees into groups. Each group must have exactly one person from Division A, two people from Division B, and three people from Division C. There are 20 people from Division A, 30 people from Division B, and 40 people from Division C at the conference. What is the smallest number of people who will not be able to be assigned to a group?
Each Group - 1 from Division A, 2 from Division B, 3 from Division C
Division A has 20 people so we can make 20 groups.
Division B has 30 people so we can make only 30/2 = 15 groups (Each group must have 2 people from B)
Division C has 40 people so we can make only 40/3 = 13 groups (Each group must have 3 people from C)
We can make only 13 groups since division C will run out of people after that.
1 from C
30 - 13*2 = 4 from B
20 - 13 = 7 from A
A total of 12 people.
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