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Question Number 176205 by otchereabdullai@gmail.com last updated on 15/Sep/22

In a school election for the positon of SRC president, one candidate obtained 87.5% of the vote cast others obtained 275 votes (a) How many votes did the winner obtain. (b) If the voter turnout was 55% find the total number of eligible voters in the school.

$$\:\mathrm{In}\:\mathrm{a}\:\mathrm{school}\:\mathrm{election}\:\mathrm{for}\:\mathrm{the}\:\mathrm{positon}\: \\ $$$$\:\:\mathrm{of}\:\mathrm{SRC}\:\mathrm{president},\:\mathrm{one}\:\mathrm{candidate} \\ $$$$\:\:\mathrm{obtained}\:\mathrm{87}.\mathrm{5\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{vote}\:\mathrm{cast}\: \\ $$$$\:\:\mathrm{others}\:\mathrm{obtained}\:\mathrm{275}\:\mathrm{votes} \\ $$$$\:\:\left(\mathrm{a}\right)\:\mathrm{How}\:\mathrm{many}\:\mathrm{votes}\:\mathrm{did}\:\mathrm{the}\:\mathrm{winner} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{obtain}. \\ $$$$\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{If}\:\mathrm{the}\:\mathrm{voter}\:\mathrm{turnout}\:\mathrm{was}\:\mathrm{55\%}\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\:\mathrm{eligible} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{voters}\:\mathrm{in}\:\mathrm{the}\:\mathrm{school}. \\ $$$$ \\ $$

Answered by Rasheed.Sindhi last updated on 15/Sep/22

Other candidates′ percentage =100−87.5=12.5% 12.5% of vote-cast=275 ((12.5)/(100))×vote-cast=275 vote-cast=275×((100)/(12.5))=2200 (a)The winner′s votes =2200−275=1925 55% of (No. of Eligible voters)=2200 ((55)/(100)) ×(No. of Eligible voters)=2200 (b)No. of Eligible voters =2200×((100)/(55))=4000

$${Other}\:{candidates}'\:\:{percentage} \\ $$$$\:\:\:\:\:\:=\mathrm{100}−\mathrm{87}.\mathrm{5}=\mathrm{12}.\mathrm{5\%} \\ $$$$\mathrm{12}.\mathrm{5\%}\:{of}\:{vote}-{cast}=\mathrm{275} \\ $$$$\frac{\mathrm{12}.\mathrm{5}}{\mathrm{100}}×{vote}-{cast}=\mathrm{275} \\ $$$${vote}-{cast}=\mathrm{275}×\frac{\mathrm{100}}{\mathrm{12}.\mathrm{5}}=\mathrm{2200} \\ $$$$\left({a}\right)\mathcal{T}{he}\:{winner}'{s}\:{votes} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2200}−\mathrm{275}=\mathrm{1925} \\ $$$$\mathrm{55\%}\:{of}\:\left({No}.\:{of}\:\mathcal{E}{ligible}\:{voters}\right)=\mathrm{2200} \\ $$$$\frac{\mathrm{55}}{\mathrm{100}}\:×\left({No}.\:{of}\:\mathcal{E}{ligible}\:{voters}\right)=\mathrm{2200} \\ $$$$\left({b}\right){No}.\:{of}\:\mathcal{E}{ligible}\:{voters} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2200}×\frac{\mathrm{100}}{\mathrm{55}}=\mathrm{4000} \\ $$$$ \\ $$

Commented by otchereabdullai@gmail.com last updated on 15/Sep/22

Am much grateful May the Almighty God bless you!

$$\mathrm{Am}\:\mathrm{much}\:\mathrm{grateful}\:\mathrm{May}\:\mathrm{the}\:\mathrm{Almighty} \\ $$$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}! \\ $$

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