High School

In an election, 2 candidates participated. 10% of the total voters did not vote. 300 votes were declared invalid. The winner gets 60% of the total votes and wins by 900 votes.

Find the number of valid votes.

A. 2700
B. 1500
C. 3700
D. 2800
E. 2900

Answer :

The number of valid votes is 2400

How to find the total number

In the election, 10% of the total voters did not vote. Therefore, the number of voters who cast their votes is 90% of the total voters. Let the total number of voters be x. Then, the number of valid votes is:

0.9x - 300

Let the number of valid votes for the winner be y. Then, the number of valid votes for the loser is:

0.9x - 300 - y

We know that the winner gets 60% of the total voters and wins by 900 votes. Therefore, we have:

y - (0.9x - 300 - y) = 900

Simplifying the expression, we get:

2y - 0.9x + 300 = 900

2y - 0.9x = 600

We also know that the total number of valid votes is equal to the difference between the total number of voters and the number of invalid votes. Therefore, we have:

0.9x - 300 + 300 = x - 300

Simplifying the expression, we get:

0.9x = x - 300

0.1x = 300

x = 3000

Substituting x = 3000 into the equation 2y - 0.9x = 600, we get:

2y - 0.9(3000) = 600

2y - 2700 = 600

2y = 3300

y = 1650

Therefore, the number of valid votes is:

0.9x - 300 = 0.9(3000) - 300 = 2400

The answer is not one of the options provided.

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