{"id":"cb_question_bank:97b9b367-2f42-49e8-a6b2-11f97e6af787","source_id":"cb_question_bank","source_item_id":"97b9b367-2f42-49e8-a6b2-11f97e6af787","external_id":"e2acc363-d0b7-4b19-ac43-34982f030a3d","ibn":null,"question_id":"0cb57740","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Each side of a 30 -sided polygon has one of three lengths. The number of sides with length 8 centimeters left parenthesis cm right parenthesis is 5 times the number of sides n with length 3 cm . There are 6 sides with length 4 cm . Which equation must be true for the value of n ?","stimulus":"","stimulus_html":null,"stem_html":"

Each side of a 30\n-sided polygon has one of three lengths. The number of sides with length 8 centimeters cm is 5\n times the number of sides n\n with length 3 cm. There are 6\n sides with length 4 cm. Which equation must be true for the value of n\n?

","rationale_html":"

Choice B is correct. It’s given that each side of a 30\n-sided polygon has one of three lengths. It's also given that the number of sides with length 8\n centimeters cm is 5\n times the number of sides n\n with length 3 cm. Therefore, there are 5×n, or \n\t5\n\tn\n\n, sides with length 8 cm. It’s also given that there are 6\n sides with length 4 cm. Therefore, the number of 3 cm, 4 cm, and 8 cm sides are n\n, 6\n, and \n\t5\n\tn\n\n, respectively. Since there are a total of 30\n sides, the equation n+6+5n=30 represents this situation. Combining like terms on the left-hand side of this equation yields 6n+6=30. Therefore, the equation that must be true for the value of n\n is 6n+6=30.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.808000+00:00","source_updated_at":"2023-08-02T20:25:59.808000+00:00","options":[{"label":"A","content_html":"

\n\t\n\t\t\n\t\t\t5\n\t\t\tn\n\t\t\n\t\t+\n\t\t6\n\t\n\t=\n\t30\n\n

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

\n\t\n\t\t\n\t\t\t6\n\t\t\tn\n\t\t\n\t\t+\n\t\t6\n\t\n\t=\n\t30\n\n

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

8n+3n+4n=30

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

85n+3n+46=30

","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}}