{"id":"cb_question_bank:de3e0efb-b5b3-4f08-991b-725e5710636b","source_id":"cb_question_bank","source_item_id":"de3e0efb-b5b3-4f08-991b-725e5710636b","external_id":"4e5c1cee-ad79-4a5a-8828-24762395ae21","ibn":null,"question_id":"038d87d7","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear 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":"A neighborhood consists of a 2 -hectare park and a 35 -hectare residential area. The total number of trees in the neighborhood is 3,934 . The equation 2 x plus 35 y equals 3,934 represents this situation. Which of the following is the best interpretation of x in this context?","stimulus":"","stimulus_html":null,"stem_html":"<p>A neighborhood consists of a <math alttext=\"2\"><mn>2</mn>\n</math>-hectare park and a <math alttext=\"35\"><mn>35</mn>\n</math>-hectare residential area. The total number of trees in the neighborhood is <math alttext=\"3,934\"><mn>3,934</mn>\n</math>. The equation <math alttext=\"2 x plus 35 y equals 3,934\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>2</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mrow>\n\t\t\t<mn>35</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>3,934</mn>\n</mrow>\n</math> represents this situation. Which of the following is the best interpretation of <em>x</em> in this context?</p>","rationale_html":"<p>Choice A is correct. It's given that a neighborhood consists of a <math alttext=\"2\"><mn>2</mn>\n</math>-hectare park and a <math alttext=\"35\"><mn>35</mn>\n</math>-hectare residential area and that the total number of trees in the neighborhood is <math alttext=\"3,934\"><mn>3,934</mn>\n</math>. It's also given that the equation <math alttext=\"2 x plus 35 y equals 3,934\"><mn>2</mn><mi>x</mi><mo>+</mo><mn>35</mn><mi>y</mi><mo>=</mo><mn>3,934</mn></math> represents this situation. Since the total number of trees for a given area can be determined by taking the number of hectares times the average number of trees per hectare, this must mean that the terms <math alttext=\"2 x\"><mrow>\n\t<mn>2</mn>\n\t<mi>x</mi>\n</mrow>\n</math> and <math alttext=\"35 y\"><mrow>\n\t<mn>35</mn>\n\t<mi>y</mi>\n</mrow>\n</math> correspond to the number of trees in the park and in the residential area, respectively. Since <math alttext=\"2 x\"><mrow>\n\t<mn>2</mn>\n\t<mi>x</mi>\n</mrow>\n</math> corresponds to the number of trees in the park, and <math alttext=\"2\"><mn>2</mn>\n</math> is the size of the park, in hectares, <math alttext=\"x\"><mi>x</mi>\n</math> must represent the average number of trees per hectare in the park.</p>\n<p>Choice B is incorrect and may result from conceptual errors.</p>\n<p>Choice C is incorrect and may result from conceptual errors.</p>\n<p>Choice D is incorrect and may result from conceptual errors.</p>","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":"<p>The average number of trees per hectare in the park</p>","ord":0},{"label":"B","content_html":"<p>The average number of trees per hectare in the residential area</p>","ord":1},{"label":"C","content_html":"<p>The total number of trees in the park</p>","ord":2},{"label":"D","content_html":"<p>The total number of trees in the residential area</p>","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}}