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Algebra / Linear equations in two variables Difficulty: Easy

A shipment consists of $5$ -pound boxes and $10$ -pound boxes with a total weight of $220$ pounds. There are $13$ $10$ -pound boxes in the shipment. How many $5$ -pound boxes are in the shipment?

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Explanation

Choice D is correct. It's given that the shipment consists of $5$ -pound boxes and $10$ -pound boxes with a total weight of $220$ pounds. Let $x$ represent the number of $5$ -pound boxes and $y$ represent the number of $10$ -pound boxes in the shipment. Therefore, the equation $5 x + 10 y = 220$ represents this situation. It's given that there are $13$ $10$ -pound boxes in the shipment. Substituting $13$ for $y$ in the equation $5 x + 10 y = 220$ yields $5 x + 10 (13) = 220$ , or $5 x + 130 = 220$ . Subtracting $130$ from both sides of this equation yields $5 x equals 90$ . Dividing both sides of this equation by $5$ yields $18$ . Thus, there are $18$ $5$ -pound boxes in the shipment.

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. This is the number of $10$ -pound boxes in the shipment.