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?

7.35 d + 6.2 s \leq 300; d \geq 2 s

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7.35 d + 6.2 s \leq 300; 2 d \geq s

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14.7 d + 6.2 s \leq 300; d \geq 2 s

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14.7 d + 6.2 s \leq 300; 2 d \geq s

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Solution

The correct option is A $7.35 d + 6.2 s \leq 300; d \geq 2 s$
There are d containers of detergents and s containers of fabric softeners. Since detergent weighs 7.35 pounds per container and softener weighs 6.2 pounds per container and total weight is capped at 300 pounds,
$7.35 d + 6.2 s \leq 300$
Further, number of containers of detergents must be at least twice as that of the number of containers of softeners. So, $d \geq 2 s$

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