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Algebra / Linear equations in two variables Difficulty: Easy

A machine makes large boxes or small boxes, one at a time, for a total of $700$ minutes each day. It takes the machine $10$ minutes to make a large box or $5$ minutes to make a small box. Which equation represents the possible number of large boxes, $x$ , and small boxes, $y$ , the machine can make each day?

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Explanation

Choice B is correct. It’s given that it takes the machine $10$ minutes to make a large box. It's also given that $x$ represents the possible number of large boxes the machine can make each day. Multiplying $10$ by $x$ gives $10 x$ , which represents the amount of time spent making large boxes. It’s given that it takes the machine $5$ minutes to make a small box. It's also given that $y$ represents the possible number of small boxes the machine can make each day. Multiplying $5$ by $y$ gives $5 y$ , which represents the amount of time spent making small boxes. Combining the amount of time spent making $x$ large boxes and $y$ small boxes yields $10 x plus 5 y$ . It’s given that the machine makes boxes for a total of $700$ minutes each day. Therefore $10 x + 5 y = 700$ represents the possible number of large boxes, $x$ , and small boxes, $y$ , the machine can make each day.

Choice A is incorrect and may result from associating the time of $10$ minutes with small, rather than large, boxes and the time of $5$ minutes with large, rather than small, boxes.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.