Candidates

The citizens of Kocúrkovo elected a mayor from two candidates. The winning candidate received 51% of all votes, which was 12 votes more than the defeated candidate received. 75% of all eligible voters came to the vote and all votes were valid.
How many citizens of Kocúrkovo voted?
How many citizens of Kocúrkovo did not come to the vote?
What % of all voters voted for the winning candidate? (round to whole percents)

Final Answer:

a =  600
b =  200
p =  38 %

Step-by-step explanation:

0.51 a = 12 + (1-0.51)·a
a = 0.75(a+b)

0.51·a = 12 + (1-0.51)·a
a = 0.75·(a+b)

0.02a = 12
0.25a-0.75b = 0

Pivot: Row 1 ↔ Row 2
0.25a-0.75b = 0
0.02a = 12

Row 2 - 0.02/0.25 · Row 1 → Row 2
0.25a-0.75b = 0
0.06b = 12


b = 12/0.06 = 200
a = 0+0.75b/0.25 = 0+0.75 · 200/0.25 = 600

a = 600
b = 200

Our linear equations calculator calculates it.

$p=100\cdot 0.51\cdot 0.75=38\%$

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