{"id":"cb_practice_pdf:t6-math-m2-q19","source_id":"cb_practice_pdf","source_item_id":"t6-math-m2-q19","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-6","module_number":2,"position":19,"stem":"Maximum number of Number of cars passengers and crew 3 174 5 284 10 559 The table shows the linear relationship between the number of cars, c, on a commuter train and the maximum number of passengers and crew, p, that the train can carry. Which equation represents the linear relationship between c and p? 55c−p = −9","stimulus":"","stimulus_html":null,"stem_html":"<p>Maximum number of Number of cars passengers and crew 3 174 5 284 10 559 The table shows the linear relationship between the number of cars, c, on a commuter train and the maximum number of passengers and crew, p, that the train can carry. Which equation represents the linear relationship between c and p? 55c−p = −9</p>","rationale_html":"<p>Choice A is correct. It’s given that there is a linear relationship between the number of cars, c, on a commuter train and the maximum number of passengers and crew, p, that the train can carry. It follows that this relationship can be = + represented by an equation of the form p mc b, where m is the rate of change of p in this relationship and b is a constant. The rate of change of p in this relationship can be calculated by dividing the difference in any two values of p by the difference in the corresponding values of c. Using two pairs of values given in 284-174 the table, the rate of change of p in this relationship is 5-3 , or 55. = + = + Substituting 55 for m in the equation p mc b yields p 55c b. The value of b can be found by substituting any value of c and its corresponding value of p 10 559 for c and p, respectively, in this equation. Substituting for c and for p 559=55 10+ 559=550+ 550 yields ^ h b, or b. Subtracting from both sides of this = = + equation yields 9 b. Substituting 9 for b in the equation p 55c b yields =55 +9 -9=55 p c . Subtracting 9 from both sides of this equation yields p c. -9=55 - Subtracting p from both sides of this equation yields c p, or 55 - =-9 c p . Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>55c−p = 9</p>","ord":0},{"label":"B","content_html":"<p>55p−c = −9</p>","ord":1},{"label":"C","content_html":"<p>55p−c = 9</p>","ord":2},{"label":"D","content_html":"","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}