Suppose there are 6 voters and 6 candidates. voters give the most preferred 3 points, the second least 2 points and the third choice 1 point. the candidate receiving the highest point total is declared the winner. find a counter-example for which the winner is not preferred by more voters than another candidate.

answer: a.

step-by-step explanation: the answer is a. because, you need to converge the fractions to find a solution.

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

hard

step-by-step explanation: