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Algebra / Linear equations in two variables Difficulty: Medium

A certain township consists of a $5$ -hectare industrial park and a $24$ -hectare neighborhood. The total number of trees in the township is $4,529$ . The equation $5 x + 24 y = 4,529$ 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 industrial park

The average number of trees per hectare in the neighborhood

The total number of trees in the industrial park

The total number of trees in the neighborhood

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Explanation

Choice A is correct. It's given that a certain township consists of a $5$ -hectare industrial park and a $24$ -hectare neighborhood and that the total number of trees in the township is $4,529$ . It's also given that the equation $5 x + 24 y = 4,529$ represents this situation. Since the total number of trees for a given area can be determined by taking the size of the area, in hectares, times the average number of trees per hectare, the best interpretation of $5 x$ is the number of trees in the industrial park and the best interpretation of $24 y$ is the number of trees in the neighborhood. Since $5$ is the size of the industrial park, in hectares, the best interpretation of $x$ is the average number of trees per hectare in the industrial 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.