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

A truck can haul a maximum weight of $5,630$ pounds. During one trip, the truck will be used to haul a $190$ -pound piece of equipment as well as several crates. Some of these crates weigh $25$ pounds each and the others weigh $62$ pounds each. Which inequality represents the possible combinations of the number of $25$ -pound crates, $x$ , and the number of $62$ -pound crates, $y$ , the truck can haul during one trip if only the piece of equipment and the crates are being hauled?

$25 x + 62 y \leq 5,440$

$25 x + 62 y \geq 5,440$

$62 x + 25 y \leq 5,630$

$62 x + 25 y \geq 5,630$

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Explanation

Choice A is correct. It's given that a truck can haul a maximum of $5,630$ pounds. It's also given that during one trip, the truck will be used to haul a $190$ -pound piece of equipment as well as several crates. It follows that the truck can haul at most $5,630 minus 190$ , or $5,440$ , pounds of crates. Since $x$ represents the number of $25$ -pound crates, the expression $25 x$ represents the weight of the $25$ -pound crates. Since $y$ represents the number of $62$ -pound crates, $62 y$ represents the weight of the $62$ -pound crates. Therefore, $25 x plus 62 y$ represents the total weight of the crates the truck can haul. Since the truck can haul at most $5,440$ pounds of crates, the total weight of the crates must be less than or equal to $5,440$ pounds, or $25 x + 62 y \leq 5,440$ .

Choice B is incorrect. This represents the possible combinations of the number of $25$ -pound crates, $x$ , and the number of $62$ -pound crates, $y$ , the truck can haul during one trip if it can haul a minimum, not a maximum, of $5,630$ pounds.

Choice C is incorrect. This represents the possible combinations of the number of $62$ -pound crates, $x$ , and the number of $25$ -pound crates, $y$ , the truck can haul during one trip if only crates are being hauled.

Choice D is incorrect. This represents the possible combinations of the number of $62$ -pound crates, $x$ , and the number of $25$ -pound crates, $y$ , the truck can haul during one trip if it can haul a minimum, not a maximum, weight of $5,630$ pounds and only crates are being hauled.