The expression 0.35 x represents the result of decreasing a positive quantity x by what percent?

Question

Accepted Answer

Choice D is correct. Let n % represent the percent by which the positive quantity x is decreased to result in 0.35 x . The value of n can be found by solving the equation x - n 100 x = 0.35 x . Since x is a common factor of each of the terms on the left-hand side of this equation, the equation can be rewritten as x 1 - n 100 = 0.35 x . Dividing each side of this equation by x yields 1 - n 100 = 0.35 . Multiplying each side of this equation by 100 yields 100 - n = 35 . Subtracting 100 from each side of this equation yields - n = - 65 . Dividing each side of this equation by - 1 yields n = 65 . Therefore, the expression 0.35 x represents the result of decreasing the positive quantity x by 65 % . Choice A is incorrect. Decreasing the quantity x by 3.5 % yields x - 0.035 x , or 0.965 x , not 0.35 x . Choice B is incorrect. Decreasing the quantity x by 35 % yields x - 0.35 x , or 0.65 x , not 0.35 x . Choice C is incorrect. Decreasing the quantity x by 6.5 % yields x - 0.065 x , or 0.935 x , not 0.35 x .

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