{"id":"cb_question_bank:206e776b-5c5d-48c0-8a74-b5bf24f4dc21","source_id":"cb_question_bank","source_item_id":"206e776b-5c5d-48c0-8a74-b5bf24f4dc21","external_id":"f02c7424-034b-4774-b41c-847249027a2e","ibn":null,"question_id":"bf4a8b6a","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A company that provides whale-watching tours takes groups of 21 people at a time. The company’s revenue is 80 dollars per adult and 60 dollars per child. If the company’s revenue for one group consisting of adults and children was 1,440 dollars, how many people in the group were children?","stimulus":"","stimulus_html":null,"stem_html":"

A company that provides whale-watching tours takes groups of 21\n people at a time. The company’s revenue is 80\n dollars per adult and 60\n dollars per child. If the company’s revenue for one group consisting of adults and children was 1,440\n dollars, how many people in the group were children?

","rationale_html":"

Choice C is correct. Let x\n represent the number of children in a whale-watching tour group. Let y\n represent the number of adults in this group. Because it's given that 21\n people are in a group and the group consists of adults and children, it must be true that x+y=21. Since the company's revenue is 60\n dollars per child, the total revenue from x\n children in this group was \n\t60\n\tx\n\n dollars. Since the company's revenue is 80\n dollars per adult, the total revenue from y\n adults in this group was \n\t80\n\ty\n\n dollars. Because it's given that the total revenue for this group was 1,440\n dollars, it must be true that 60x+80y=1,440. The equations x+y=21 and 60x+80y=1,440 form a linear system of equations that can be solved to find the value of x\n, which represents the number of children in the group, using the elimination method. Multiplying both sides of the equation x+y=21 by 80\n yields 80x+80y=1,680. Subtracting 60x+80y=1,440 from 80x+80y=1,680 yields (80x+80y)-(60x+80y)=1,680-1,440, which is equivalent to 80x-60x+80y-80y=240, or 20x=240. Dividing both sides of this equation by 20\n yields x=12. Therefore, 12\n people in the group were children.

\n

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

\n

Choice B is incorrect. This is the number of adults in the group, not the number of children in the group.

\n

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

","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.816000+00:00","source_updated_at":"2023-08-02T20:25:59.816000+00:00","options":[{"label":"A","content_html":"

3\n

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

9\n

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

12\n

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

18\n

","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}}