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Linear equations in two variables SAT question

Math · Algebra · Medium · Answer it here, explanation included.

In an article about exercise, it is estimated that a 160-pound adult uses 200 calories for every 30 minutes of hiking and 150 calories for every 30 minutes of bicycling. An adult who weighs 160 pounds has completed 1 hour of bicycling. Based on the article, how many hours should the adult hike to use a total of 1,900 calories from bicycling and hiking?

ExplanationShow

Choice D is correct. Since a 160-pound adult uses 200 calories for every 30 minutes of hiking, then the same adult uses $200 h$ calories after hiking for h 30-minute periods. Similarly, the same adult uses $150 b$ calories after bicycling for b 30-minute periods. Therefore, the equation $200 h plus 150 b, equals 1,900$ represents the situation where a 160-pound adult uses a total of 1,900 calories from hiking for h 30-minute periods and bicycling for b 30-minute periods. It’s given that the adult completes 1 hour, or 2 30-minute periods, of bicycling. Substituting 2 for b in the equation $200 h plus 150 b, equals 1,900$ yields $200 h plus, 150 times 2, equals 1,900$ , or $200 h plus 300, equals 1,900$ . Subtracting 300 from both sides of this equation yields $200 h equals 1,600$ . Dividing both sides by 200 yields $h equals 8$ . Since h represents the number of 30-minute periods spent hiking and there are 2 30-minute periods in every hour, it follows that the adult will need to hike for $the fraction eight over 2$ , or 4 hours to use a total of 1,900 calories from bicycling and hiking.

Choice A is incorrect and may result from solving the equation $200 h equals 1,900$ . This represents 0 30-minute periods bicycling instead of 2. Choice B is incorrect and may result from solving the equation $200 h plus 150, equals 1,900$ . This represents 1 30-minute period of bicycling instead of 2. Choice C is incorrect. This may result from determining that the number of 30-minute periods the adult should hike is 8, but then subtracting 2 from 8, rather than dividing 8 by 2, to find the number of hours the adult should hike.

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Linear equations in two variables SAT question

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