In a recent student body election, Adam received 40 more than 40% of the votes. Brigitte received 40 less
than 50% of the number Adam received. Carl received 20 more than 50% of what Brigitte received, and
Diane received the remaining 180 votes. How many votes were cast in the election and who was the
winner?

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mixter17 mixter17 · Answer 1 · 2019-12-23T21:38:34+01:00

The total vote cast was 700.

The winner was Adam (received 320 votes)

Why?

To solve the problem, we need to make equations to express the number of votes received for each of the candidates.

Solving we have:

Let be "v" the total vote cast,

For Adam,

[tex]A=40+0.4*v[/tex]

For Brigitte,

[tex]B=0.5(40+0.4v)-40[/tex]

[tex]B=20+0.2v-40[/tex]

[tex]B=0.2v-20[/tex]

For Carl,

[tex]C=20+0.5*B[/tex]

[tex]C=20+0.5*(0.2v-20)[/tex]

[tex]C=10+0.1v[/tex]

For Diane,

[tex]D=180votes[/tex]

Now, the total vote cast will be:

[tex]v=A+B+C+D\\\\v=(40+0.4v)+(0.2v-20)+(10+0.1v)+180\\\\v=(40-20+10+180)+(0.4v+0.2v+0.1v)[/tex]

[tex]v=210+0.7v\\\\v-0.7v=210\\\\v=\frac{210}{0.3}=700[/tex]

Now, substituting "v" in each equation to calculate the number of votes for each candidate, we have:

[tex]Adam=40+0.4*700=320votes\\Brigitte=0.2*700-20=120votes\\Carl=10+0.1*700=80votes\\Diane=180votes[/tex]

Hence, we have that the total vote cast was 700, and the winner was Adam (received 320 votes)

Have a nice day!