{"id":"cb_question_bank:0b746561-2736-4f1e-abf9-351fea4e81f6","source_id":"cb_question_bank","source_item_id":"0b746561-2736-4f1e-abf9-351fea4e81f6","external_id":"d4043654-05ea-4067-80ff-0c1687134c44","ibn":null,"question_id":"686b7244","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A certain apprentice has enrolled in 85 hours of training courses. The equation 10 x plus 15 y equals 85 represents this situation, where x is the number of on-site training courses and y is the number of online training courses this apprentice has enrolled in. How many more hours does each online training course take than each on-site training course?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A certain apprentice has enrolled in <math alttext=\"85\"><mn>85</mn>\n</math> hours of training courses. The equation <math alttext=\"10 x plus 15 y equals 85\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>10</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>15</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>85</mn>\n</mrow>\n</math> represents this situation, where <math alttext=\"x\"><mi>x</mi>\n</math> is the number of on-site training courses and <math alttext=\"y\"><mi>y</mi>\n</math> is the number of online training courses this apprentice has enrolled in. How many more hours does each online training course take than each on-site training course?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"5\"><mn>5</mn>\n</math>. It's given that the equation <math alttext=\"10 x plus 15 y equals 85\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>10</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>15</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>85</mn>\n</mrow>\n</math> represents the situation, where <math alttext=\"x\"><mi>x</mi>\n</math> is the number of on-site training courses, <math alttext=\"y\"><mi>y</mi>\n</math> is the number of online training courses, and <math alttext=\"85\"><mn>85</mn>\n</math> is the total number of hours of training courses the apprentice has enrolled in. Therefore, <math alttext=\"10 x\"><mrow>\n\t<mn>10</mn>\n\t<mi>x</mi>\n</mrow>\n</math> represents the number of hours the apprentice has enrolled in on-site training courses, and <math alttext=\"15 y\"><mrow>\n\t<mn>15</mn>\n\t<mi>y</mi>\n</mrow>\n</math> represents the number of hours the apprentice has enrolled in online training courses. Since <math alttext=\"x\"><mi>x</mi>\n</math> is the number of on-site training courses and <math alttext=\"y\"><mi>y</mi>\n</math> is the number of online training courses the apprentice has enrolled in, <math alttext=\"10\"><mn>10</mn>\n</math> is the number of hours each on-site course takes and <math alttext=\"15\"><mn>15</mn>\n</math> is the number of hours each online course takes. Subtracting these numbers gives <math alttext=\"15 minus 10\"><mn>15</mn><mo>-</mo><mn>10</mn></math>, or <math alttext=\"5\"><mn>5</mn>\n</math> more hours each online training course takes than each on-site training course.</p>","correct_answer":["5"],"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":[],"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}}