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Algebra / Linear equations in two variables Difficulty: Medium

A neighborhood consists of a $2$ -hectare park and a $35$ -hectare residential area. The total number of trees in the neighborhood is $3,934$ . The equation $2 x + 35 y = 3,934$ represents this situation. Which of the following is the best interpretation of x in this context?

The average number of trees per hectare in the park

The average number of trees per hectare in the residential area

The total number of trees in the park

The total number of trees in the residential area

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Explanation

Choice A is correct. It's given that a neighborhood consists of a $2$ -hectare park and a $35$ -hectare residential area and that the total number of trees in the neighborhood is $3,934$ . It's also given that the equation $2 x + 35 y = 3,934$ represents this situation. Since the total number of trees for a given area can be determined by taking the number of hectares times the average number of trees per hectare, this must mean that the terms $2 x$ and $35 y$ correspond to the number of trees in the park and in the residential area, respectively. Since $2 x$ corresponds to the number of trees in the park, and $2$ is the size of the park, in hectares, $x$ must represent the average number of trees per hectare in the park.

Choice B is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.