A total of 364 paper straws of equal length were used to construct two types of polygons: triangles and rectangles.

Question

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 x , y = 24 , 73 in this context?

Accepted Answer

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 x , y = 24 , 73 means that if x = 24 , then y = 73 . Substituting 24 for x and 73 for y in 3 x + 4 y = 364 yields 3 24 + 4 73 = 364 , or 364 = 364 , which is true. Therefore, in this context, the equation x , y = 24 , 73 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.

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