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

A certain elephant weighs 200 pounds at birth and gains more than 2 but less than 3 pounds per day during its first year. Which of the following inequalities represents all possible weights w, in pounds, for the elephant 365 days after birth?

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Explanation

Choice D is correct. It’s given that the elephant weighs 200 pounds at birth and gains more than 2 pounds but less than 3 pounds per day during its first year. The inequality $200 plus 2 d, is less than w, which is less than 200 plus 3 d$ represents this situation, where d is the number of days after birth. Substituting 365 for d in the inequality gives $200 plus 2, times 365, is less than w, which is less than 200 plus 3, times 365$ , or $930 is less than w, which is less than 1,295$ .

Choice A is incorrect and may result from solving the inequality $200 times 2, is less than w, which is less than 200 times 3$ . Choice B is incorrect and may result from solving the inequality for a weight range of more than 1 pound but less than 2 pounds: $200 plus 1, times 365, is less than w, which is less than 200 plus 2, times 365$ . Choice C is incorrect and may result from calculating the possible weight gained by the elephant during the first year without adding the 200 pounds the elephant weighed at birth.