A piece of cloth costs 10,000. If a 2 m longer piece of the same cloth is purchased for the same amount, it would cost 250 less per metre. What is the original length of the piece of cloth?

Explanation

Let original length be x. \frac{10000}{x} - \frac{10000}{x+2} = 250. Dividing by 250 yields \frac{40}{x} - \frac{40}{x+2} = 1 \implies 40(x+2) - 40x = x(x+2) \implies x^2 + 2x - 80 = 0. Solving gives x=8.

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