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In an election, 1200 total votes were cast for the 3 candidates. The second-place candidate received 155 fewer votes than the winner and 200 votes more than the third-place candidate. How many votes did the winner receive

Respuesta :

The winner received 570 votes.

Let the winner candidate be c1

Let the  second-place candidate be c2

Let the  third-place candidate be c3

[tex]c2=c1-155\\[/tex].........equation 1

[tex]c2=c3+200\\[/tex]

[tex]c3=c2-200 \\[/tex]

[tex]c3=c1-155-200\\[/tex].........by equation 1

[tex]c3=c1-355[/tex]........equation 2

Now we know,

[tex]c1+c2+c3=1200[/tex]

[tex]c1+(c1-155)+(c1-355)=1200[/tex] .....by equations 1 and 2

[tex]3c1-510=1200[/tex]

[tex]3c1=1200+510\\3c1=170\\c1=570[/tex]

Hence, The winner received 570 votes.

Learn more about equations here https://brainly.com/question/16192514

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