{"id":"cb_question_bank:c50e248a-9b34-4d83-9ce2-2dcf53c4f023","source_id":"cb_question_bank","source_item_id":"c50e248a-9b34-4d83-9ce2-2dcf53c4f023","external_id":"61a4ffe2-81eb-435b-bda6-4f44122ffded","ibn":null,"question_id":"c5479c1a","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"E","score_band":1,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A shipment consists of 5 -pound boxes and 10 -pound boxes with a total weight of 220 pounds. There are 13 10 -pound boxes in the shipment. How many 5 -pound boxes are in the shipment?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A shipment consists of <math alttext=\"5\"><mn>5</mn>\n</math>-pound boxes and <math alttext=\"10\"><mn>10</mn>\n</math>-pound boxes with a total weight of <math alttext=\"220\"><mn>220</mn>\n</math> pounds. There are <math alttext=\"13\"><mn>13</mn>\n</math> <math alttext=\"10\"><mn>10</mn>\n</math>-pound boxes in the shipment. How many <math alttext=\"5\"><mn>5</mn>\n</math>-pound boxes are in the shipment?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. It's given that the shipment consists of <math alttext=\"5\"><mn>5</mn>\n</math>-pound boxes and <math alttext=\"10\"><mn>10</mn>\n</math>-pound boxes with a total weight of <math alttext=\"220\"><mn>220</mn>\n</math> pounds. Let <math alttext=\"x\"><mi>x</mi>\n</math> represent the number of <math alttext=\"5\"><mn>5</mn>\n</math>-pound boxes and <math alttext=\"y\"><mi>y</mi>\n</math> represent the number of <math alttext=\"10\"><mn>10</mn>\n</math>-pound boxes in the shipment. Therefore, the equation <math alttext=\"5 x plus 10 y equals 220\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>5</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>10</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>220</mn>\n</mrow>\n</math> represents this situation. It's given that there are <math alttext=\"13\"><mn>13</mn>\n</math> <math alttext=\"10\"><mn>10</mn>\n</math>-pound boxes in the shipment. Substituting <math alttext=\"13\"><mn>13</mn>\n</math> for <math alttext=\"y\"><mi>y</mi>\n</math> in the equation <math alttext=\"5 x plus 10 y equals 220\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>5</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>10</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>220</mn>\n</mrow>\n</math> yields <math alttext=\"5 x plus 10 left parenthesis 13 right parenthesis equals 220\"><mn>5</mn><mi>x</mi><mo>+</mo><mn>10</mn><mfenced><mn>13</mn></mfenced><mo>=</mo><mn>220</mn></math>, or <math alttext=\"5 x plus 130 equals 220\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>5</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>130</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>220</mn>\n</mrow>\n</math>. Subtracting <math alttext=\"130\"><mn>130</mn>\n</math> from both sides of this equation yields <math alttext=\"5 x equals 90\"><mrow>\n\t<mrow>\n\t\t<mn>5</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>90</mn>\n</mrow>\n</math>. Dividing both sides of this equation by <math alttext=\"5\"><mn>5</mn>\n</math> yields <math alttext=\"18\"><mn>18</mn>\n</math>. Thus, there are <math alttext=\"18\"><mn>18</mn>\n</math> <math alttext=\"5\"><mn>5</mn>\n</math>-pound boxes in the shipment.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This is the number of <math alttext=\"10\"><mn>10</mn>\n</math>-pound boxes in the shipment.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.813000+00:00","source_updated_at":"2023-08-02T20:25:59.813000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"5\"><mn>5</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"10\"><mn>10</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"13\"><mn>13</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"18\"><mn>18</mn>\n</math></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}}