A machine makes large boxes or small boxes, one at a time, for a total of 700 minutes each day.

Question

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?

A.

$5 x + 10 y = 700$

B.

$10 x + 5 y = 700$

C.

$(x + y) (10 + 5) = 700$

D.

$(10 + x) (5 + y) = 700$

Accepted Answer

Choice B is correct. It&rsquo;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&rsquo;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 + 5 y . It&rsquo;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.

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