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Of the votes cast on a certain proposal, 80 more were in

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Of the votes cast on a certain proposal, 80 more were in

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Of the votes cast on a certain proposal, 80 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)

A. 480
B. 400
C. 300
D. 240
E. 160

OA B.

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Vote against the proposal = 40% of the Total votes
Vote for the proposal = 100 - 40 = 60% of the Total vote
Total vote is unknown
$$Let\ total\ vote\ =\ x$$
of the total vote x, 80 more were in favor of the proposal than were against it ; thus
$$\left(60\%\ of\ \ x\right)-\left(40\%\ of\ x\right)=80$$
$$\left(\frac{60}{100}\cdot x\right)-\left(\frac{40}{100}-x\right)=80$$
$$0.6x-0.4x=80$$
$$0.2x=80$$
dividing both sides by the coefficient of x
$$\frac{0.2x}{0.2}=\frac{80}{0.2}$$
$$x=400$$
$$answer\ is\ Option\ B$$

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