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Algebra / Linear functions Difficulty: Hard

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?

$S = \frac{w}{170}$

$upper S equals 170 w$

$upper S equals 340 w$

$S = \frac{w}{85}$

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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 to cover $2 w$ square feet. It’s also given that one gallon of stain will cover $170$ 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 gallons of stain that will be needed. Dividing $2 w$ by $170$ yields $StartFraction 2 w Over 170 EndFraction$ , or $StartFraction w Over 85 EndFraction$ . Therefore, the equation that represents the total amount of stain $S$ , in gallons, needed to stain the fence of the yard twice is $S = \frac{w}{85}$ .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.