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One gallon of stain will cover 170 square feet of a surface. A yard has a total fence area of w square feet. Which equation represents the total amount of stain S, in gallons, needed to stain the fence in this yard twice? S =
Correct answer: D (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice D is correct. It’s given that w represents the total fence area, in square feet. Since the fence will be stained twice, the amount of stain, in gallons, will need 170 to cover 2w square feet. It’s also given that one gallon of stain will cover square feet. Dividing the total area, in square feet, of the surface to be stained by the number of square feet covered by one gallon of stain gives the number of 170 2 gallons of stain that will be needed. Dividing 2w by yields 17w0, or 8w5. Therefore, the equation that represents the total amount of stain S, in gallons, needed to stain the fence of the yard twice is S = 8w5. Choice A is incorrect. This equation represents the total amount of stain, in gallons, needed to stain the fence once, not twice. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.
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