In the weighted voting system 12: 8, 6, 3, 3, 1.
a. how many players are there in the system?
b. how many total votes are there in the system?
c. what is the quota for the system?
d. how many votes does p1 have?

The answer is as follows:

Step-by-step explanation:

In the weighted voting system 12: 8, 6, 3, 3, 1

(a) There are 5 players who cast there votes:

P1 : 8 votes

P2: 6 votes

P3: 3 votes

P4: 3 Votes

P5: 1 Votes

(b) so, there are 21 votes in total.

(c) Here, quota means that for a meaningful weighted voting, quota is the majority of votes for a decision to be made. So, quota must be more than half of the total number of votes for making any decision.

∴ Quota for this question = 12

(d) Player 1 (P1) is having maximum number of votes and that is 8 votes.

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4