Multiple choice

By selling a sewing machine for $24, a man makes as much % of profit as the cost price. What is the cost price?

  1. $20
  2. $10
  3. $15
  4. $25
  5. $18
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A Correct answer
Explanation

Let CP = x. Profit % = x. Selling Price = CP + (Profit % of CP) = x + (x/100)*x = 24. x^2/100 + x - 24 = 0. x^2 + 100x - 2400 = 0. (x+120)(x-20) = 0. x = 20.

AI explanation

Let the cost price of the sewing machine be x dollars. The profit is also x percent of the cost price, meaning the profit amount is (x/100) times x, which simplifies to x^2/100. The selling price equals the cost price plus the profit, giving the equation x + x^2/100 = 24. Multiplying by 100 gives the quadratic equation x^2 + 100x - 2400 = 0, which factors to (x + 120)(x - 20) = 0. Discarding the negative value, the cost price x is $20.

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