{"id":"cb_question_bank:3e2d4b19-6748-4ee5-96c8-43143d5a851a","source_id":"cb_question_bank","source_item_id":"3e2d4b19-6748-4ee5-96c8-43143d5a851a","external_id":"135d0742-47f5-4297-a337-b8715edbb016","ibn":null,"question_id":"95ed0b69","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"p equals StartFraction k Over 4 j plus 9 EndFraction The given equation relates the distinct positive numbers p , k , and j . Which equation correctly expresses 4 j plus 9 in terms of p and k ?","stimulus":"","stimulus_html":null,"stem_html":"

\n\tp\n\t=\n\t\n\t\t\n\t\t\tk\n\t\t\t\n\t\t\t\t\n\t\t\t\t\t4\n\t\t\t\t\tj\n\t\t\t\t\n\t\t\t\t+\n\t\t\t\t9\n\t\t\t\n\t\t\n\t\n\n

\n

The given equation relates the distinct positive numbers p\n, k\n, and j\n. Which equation correctly expresses \n\t\n\t\t4\n\t\tj\n\t\n\t+\n\t9\n\n in terms of p\n and k\n?

","rationale_html":"

Choice A is correct. To express 4j+9 in terms of p\n and k\n, the given equation must be solved for 4j+9. Since it's given that j\n is a positive number, 4j+9 is not equal to zero. Therefore, multiplying both sides of the given equation by 4j+9 yields the equivalent equation p4j+9=k. Since it's given that p\n is a positive number, p\n is not equal to zero. Therefore, dividing each side of the equation p4j+9=k by p\n yields the equivalent equation 4j+9=kp.

\n

Choice B is incorrect. This equation is equivalent to p=4j+9k.

\n

Choice C is incorrect. This equation is equivalent to p=k-4j-9.

\n

Choice D is incorrect. This equation is equivalent to p=k4j+9.

","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.824000+00:00","source_updated_at":"2023-08-02T20:25:59.824000+00:00","options":[{"label":"A","content_html":"

\n\t\n\t\t\n\t\t\t4\n\t\t\tj\n\t\t\n\t\t+\n\t\t9\n\t\n\t=\n\t\n\t\t\n\t\t\tk\n\t\t\tp\n\t\t\n\t\n\n

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

\n\t\n\t\t\n\t\t\t4\n\t\t\tj\n\t\t\n\t\t+\n\t\t9\n\t\n\t=\n\t\n\t\tk\n\t\tp\n\t\n\n

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

4j+9=k-p

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

\n\t\n\t\t\n\t\t\t4\n\t\t\tj\n\t\t\n\t\t+\n\t\t9\n\t\n\t=\n\t\n\t\t\n\t\t\tp\n\t\t\tk\n\t\t\n\t\n\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}}