SOLUTION: Can you help me answer this? Thanks In a country then are 100 governors, every governor has 4 assistants. Every governor and assistant serve various committees. Each committee may

Question 1006385: Can you help me answer this? Thanks
In a country then are 100 governors, every governor has 4 assistants. Every governor and assistant serve various committees. Each committee may be composed of 5 governors, 4 governors and 4 assistants, or 2 governors and 12 assistants. Each governor serves 5 committees, and each assistant serves 3 committees. How many committees are there?
a. 60
b. 80
c. 100
d. 120
e. 160
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
There is a total of assistants,
and each will serve in exactly committees,
so we will prepare assistant place cards.
= number of committees made up of 2 governors and 12 assistants.
= number of committees made up of 4 governors and 2 assistants.
number of assistant place cards prepared for the committees with assistants.
Since each of the governors serve in exactly committees,
we will prepare governor place cards.
For those place cards to suffice for the committees with assistants, we need
.
We have the system ,which graphs as
We need to be in the green-dashed region and on the red line.
If we do not set up any 5-governor committees,
-->--> .
So, forming committees, including
committees made up of 2 governors and 12 assistants, and
committees made up of 4 governors and 2 assistants,
seems a possibility.
We could rearrange the committees differently, getting rid
Setting up 5-governor meetings sounds like it would lead to less meetings.
However, as shown by common sense , and by <--> ,
for every extra 12-assistant committee, we must give up 4-assistant committees,
for a total of less committees with assistants.
using more governor place cards for the extra 12-assistant committee,
and requiring less governor place cards for the eliminated 4-assistant committees.
That would leave us with governor place cards,
which would be used in 5-governor committee.
That way, every time we do that shift,
we eliminate a total of committees with assistants,
but create 5-governor committees,
leaving the total number of committees always at .

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