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Select the correct answerIn a college election between two students, 10% of the votes cast are invalid. The winner gets 70% of the valid votes and defeats the loser by 1800 votes. How many votes were totally cast?Options7,2001,8005,0003,600

Question

Select the correct answerIn a college election between two students, 10% of the votes cast are invalid. The winner gets 70% of the valid votes and defeats the loser by 1800 votes. How many votes were totally cast?Options7,2001,8005,0003,600

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Solution

Let's solve this step by step:

  1. Let's assume the total votes cast were x.
  2. According to the problem, 10% of the votes cast are invalid. So, the valid votes are 90% of x, which is 0.9x.
  3. The winner gets 70% of the valid votes, which is 0.7 * 0.9x = 0.63x.
  4. The loser gets the remaining valid votes, which is 0.9x - 0.63x = 0.27x.
  5. The winner defeats the loser by 1800 votes. So, 0.63x - 0.27x = 1800.
  6. Solving the above equation, we get 0.36x = 1800.
  7. Dividing both sides by 0.36, we get x = 1800 / 0.36 = 5000.

So, the total votes cast were 5000.

This problem has been solved

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