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Algebra / Linear equations in two variables Difficulty: Easy

A total of $364$ paper straws of equal length were used to construct two types of polygons: triangles and rectangles. The triangles and rectangles were constructed so that no two polygons had a common side. The equation $3 x + 4 y = 364$ represents this situation, where $x$ is the number of triangles constructed and $y$ is the number of rectangles constructed. What is the best interpretation of $left parenthesis x comma y right parenthesis equals left parenthesis 24 comma 73 right parenthesis$ in this context?

If $24$ triangles were constructed, then $73$ rectangles were constructed.

If $24$ triangles were constructed, then $73$ paper straws were used.

If $73$ triangles were constructed, then $24$ rectangles were constructed.

If $73$ triangles were constructed, then $24$ paper straws were used.

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Explanation

Choice A is correct. It's given that $364$ paper straws of equal length were used to construct triangles and rectangles, where no two polygons had a common side. It's also given that the equation $3 x + 4 y = 364$ represents this situation, where $x$ is the number of triangles constructed and $y$ is the number of rectangles constructed. The equation $left parenthesis x comma y right parenthesis equals left parenthesis 24 comma 73 right parenthesis$ means that if $x equals 24$ , then $y equals 73$ . Substituting $24$ for $x$ and $73$ for $y$ in $3 x + 4 y = 364$ yields $3 (24) + 4 (73) = 364$ , or $364 equals 364$ , which is true. Therefore, in this context, the equation $left parenthesis x comma y right parenthesis equals left parenthesis 24 comma 73 right parenthesis$ means that if $24$ triangles were constructed, then $73$ rectangles were constructed.

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.