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Problem-Solving and Data Analysis / Ratios, rates, proportional relationships, and units Difficulty: Hard

A landscaper uses a hose that puts $88 x$ ounces of water in a bucket in $5 y$ minutes. Which expression represents the number of ounces of water the hose puts in the bucket in $9 y$ minutes at this rate?

$StartFraction 9 x Over 440 EndFraction$

$StartFraction 440 x Over 9 EndFraction$

$StartFraction 5 x Over 792 EndFraction$

$StartFraction 792 x Over 5 EndFraction$

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Explanation

Choice D is correct. It’s given that a hose puts $88 x$ ounces of water in a bucket in $5 y$ minutes. Therefore, the rate at which the hose puts water in the bucket, in ounces per minute, can be represented by the expression $StartFraction 88 x Over 5 y EndFraction$ . Let $w$ represent the number of ounces of water the hose puts in the bucket in $9 y$ minutes at this rate. It follows that the rate at which the hose puts water in the bucket, in ounces per minute, can be represented by the expression $StartFraction w Over 9 y EndFraction$ . The expressions $StartFraction 88 x Over 5 y EndFraction$ and $StartFraction w Over 9 y EndFraction$ represent the same rate, so it follows that $\frac{88 x}{5 y} = \frac{w}{9 y}$ . Multiplying both sides of this equation by $9 y$ yields $\frac{792 x y}{5 y} = w$ , or $\frac{792 x}{5} = w$ . Therefore, the number of ounces of water the hose puts in the bucket in $9 y$ minutes can be represented by the expression $StartFraction 792 x Over 5 EndFraction$ .

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

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

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