{"id":"cb_question_bank:39869964-a3c6-41ac-8822-edb03f4aa034","source_id":"cb_question_bank","source_item_id":"39869964-a3c6-41ac-8822-edb03f4aa034","external_id":"aaebe46b-7143-4bb9-ae10-3f9ce2a0fbcb","ibn":null,"question_id":"c6b151d4","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"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 plus 4 y equals 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?","stimulus":"","stimulus_html":null,"stem_html":"

A total of 364\n 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 \n\t\n\t\t\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t4\n\t\t\ty\n\t\t\n\t\n\t=\n\t364\n\n represents this situation, where x\n is the number of triangles constructed and y\n is the number of rectangles constructed. What is the best interpretation of x,y=24,73 in this context?

","rationale_html":"

Choice A is correct. It's given that 364\n 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 3x+4y=364 represents this situation, where x\n is the number of triangles constructed and y\n is the number of rectangles constructed. The equation x,y=24,73 means that if x=24, then y=73. Substituting 24\n for x\n and 73\n for y\n in 3x+4y=364 yields 324+473=364, or 364=364, which is true. Therefore, in this context, the equation x,y=24,73 means that if 24\n triangles were constructed, then 73\n rectangles were constructed. 

\n

Choice B is incorrect and may result from conceptual errors.

\n

Choice C is incorrect and may result from conceptual errors.

\n

Choice D is incorrect and may result from conceptual errors.

","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.814000+00:00","source_updated_at":"2023-08-02T20:25:59.814000+00:00","options":[{"label":"A","content_html":"

If 24\n triangles were constructed, then 73\n rectangles were constructed.

","ord":0},{"label":"B","content_html":"

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

","ord":1},{"label":"C","content_html":"

If 73\n triangles were constructed, then 24\n rectangles were constructed.

","ord":2},{"label":"D","content_html":"

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

","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}