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Linear equations in two variables SAT question

Math · Algebra · Easy · Answer it here, explanation included.

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?

ExplanationShow

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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Linear equations in two variables SAT question

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