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

A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

A. $7 point three five d, plus, 6 point 2 s, is less than or equal to 300, and, d is greater than or equal to 2 s$

B. $7 point three five d, plus, 6 point 2 s, is less than or equal to 300, and, 2 d is greater than or equal to s$

C. $14 point 7 d, plus, 6 point 2 s, is less than or equal to 300, and, d is greater than or equal to 2 s$

D. $14 point 7 d, plus, 6 point 2 s, is less than or equal to 300, and, 2 d is greater than or equal to s$

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Explanation

Choice A is correct. The number of containers in a shipment must have a weight less than or equal to 300 pounds. The total weight, in pounds, of detergent and fabric softener that the supplier delivers can be expressed as the weight of each container multiplied by the number of each type of container, which is 7.35d for detergent and 6.2s for fabric softener. Since this total cannot exceed 300 pounds, it follows that $7 point 3 5 d, plus 6 point 2 s, is less than or equal to 300$ . Also, since the laundry service wants to buy at least twice as many containers of detergent as containers of fabric softener, the number of containers of detergent should be greater than or equal to two times the number of containers of fabric softener. This can be expressed by the inequality $d is greater than or equal to 2 s$ .

Choice B is incorrect because it misrepresents the relationship between the numbers of each container that the laundry service wants to buy. Choice C is incorrect because the first inequality of the system incorrectly doubles the weight per container of detergent. The weight of each container of detergent is 7.35, not 14.7 pounds. Choice D is incorrect because it doubles the weight per container of detergent and transposes the relationship between the numbers of containers.