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Algebra / Linear inequalities in one or two variables Difficulty: Easy

A geologist estimates that the volume of a slab of granite is greater than $12.7$ cubic feet but less than $15.7$ cubic feet. The geologist also estimates that the slab of granite weighs $165$ pounds per cubic foot of volume. Which inequality represents this situation, where $x$ represents the estimated total weight, in pounds, of the slab of granite?

$165 - 15.7 < x < 165 - 12.7$

$165 + 12.7 < x < 165 + 15.7$

$165 left parenthesis 12.7 right parenthesis less than x less than 165 left parenthesis 15.7 right parenthesis$

$\frac{165}{15.7} < x < \frac{165}{12.7}$

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Explanation

Choice C is correct. It's given that the estimated volume of the slab of granite is greater than $12.7$ cubic feet but less than $15.7$ cubic feet. It's also given that the estimated weight per cubic foot of volume of that slab is $165$ pounds. The estimated total weight of the slab of granite, in pounds, can be calculated by multiplying the estimated volume by the estimated weight per cubic foot. Therefore, if the estimated volume of the slab of granite is $12.7$ cubic feet, its estimated total weight is $165 left parenthesis 12.7 right parenthesis$ pounds, and if the estimated volume of the slab of granite is $15.7$ cubic feet, its estimated total weight is $165 left parenthesis 15.7 right parenthesis$ pounds. Since the estimated volume of the slab of granite is greater than $12.7$ cubic feet but less than $15.7$ cubic feet, the estimated total weight $x$ , in pounds, must be greater than $165 left parenthesis 12.7 right parenthesis$ pounds and less than $165 left parenthesis 15.7 right parenthesis$ pounds. This situation can be represented by the inequality $165 left parenthesis 12.7 right parenthesis less than x less than 165 left parenthesis 15.7 right parenthesis$ .

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 D is incorrect and may result from conceptual or calculation errors.