{"id":"cb_question_bank:f6530365-1201-4f1a-819d-f84c60eb57f6","source_id":"cb_question_bank","source_item_id":"f6530365-1201-4f1a-819d-f84c60eb57f6","external_id":"62a434cb-ba25-40cd-9fae-dadf2a410594","ibn":null,"question_id":"768b2425","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Last week, an interior designer earned a total of dollar sign 1,258 from consulting for x hours and drawing up plans for y hours. The equation 68 x plus 85 y equals 1,258 represents this situation. Which of the following is the best interpretation of 68 in this context?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Last week, an interior designer earned a total of <math alttext=\"dollar sign 1,258\"><mo>$</mo><mn>1,258</mn></math>&nbsp;from consulting for <math alttext=\"x\"><mi>x</mi>\n</math> hours and drawing up plans for <math alttext=\"y\"><mi>y</mi>\n</math> hours. The equation&nbsp;<math alttext=\"68 x plus 85 y equals 1,258\"><mn>68</mn><mi>x</mi><mo>+</mo><mn>85</mn><mi>y</mi><mo>=</mo><mn>1,258</mn></math> represents this situation. Which of the following is the best interpretation of <math alttext=\"68\"><mn>68</mn>\n</math> in this context?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It's given that&nbsp;<math alttext=\"68 x plus 85 y equals 1,258\"><mn>68</mn><mi>x</mi><mo>+</mo><mn>85</mn><mi>y</mi><mo>=</mo><mn>1,258</mn></math> represents the situation where an interior designer earned a total of&nbsp;<math alttext=\"dollar sign 1,258\"><mo>$</mo><mn>1,258</mn></math> last week from consulting for <math alttext=\"x\"><mi>x</mi>\n</math> hours and drawing up plans for <math alttext=\"y\"><mi>y</mi>\n</math> hours. Thus, <math alttext=\"68 x\"><mrow>\n\t<mn>68</mn>\n\t<mi>x</mi>\n</mrow>\n</math> represents the amount earned, in dollars, from consulting for <math alttext=\"x\"><mi>x</mi>\n</math> hours, and <math alttext=\"85 y\"><mrow>\n\t<mn>85</mn>\n\t<mi>y</mi>\n</mrow>\n</math> represents the amount earned, in dollars, from drawing up plans for <math alttext=\"y\"><mi>y</mi>\n</math> hours. Since <math alttext=\"68 x\"><mrow>\n\t<mn>68</mn>\n\t<mi>x</mi>\n</mrow>\n</math> represents the amount earned, in dollars, from consulting for <math alttext=\"x\"><mi>x</mi>\n</math> hours, it follows that the interior designer earned <math alttext=\"dollar sign 68\"><mo>$</mo><mn>68</mn></math> per hour consulting last week.</p>\n<p>Choice B is incorrect. The interior designer worked <math alttext=\"y\"><mi>y</mi>\n</math> hours, not <math alttext=\"68\"><mn>68</mn>\n</math> hours, drawing up plans last week.</p>\n<p>Choice C is incorrect. The interior designer earned&nbsp;<math alttext=\"dollar sign 85\"><mo>$</mo><mn>85</mn></math> per hour, not&nbsp;<math alttext=\"dollar sign 68\"><mo>$</mo><mn>68</mn></math> per hour, drawing up plans last week.</p>\n<p>Choice D is incorrect. The interior designer worked <math alttext=\"x\"><mi>x</mi>\n</math> hours, not <math alttext=\"68\"><mn>68</mn>\n</math> hours, consulting last week.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.814000+00:00","source_updated_at":"2023-08-02T20:25:59.814000+00:00","options":[{"label":"A","content_html":"<p style=\"text-align: left;\">The interior designer earned <math alttext=\"dollar sign 68\"><mo>$</mo><mn>68</mn></math> per hour consulting last week.</p>","ord":0},{"label":"B","content_html":"<p style=\"text-align: left;\">The interior designer worked <math alttext=\"68\"><mn>68</mn>\n</math> hours drawing up plans last week.</p>","ord":1},{"label":"C","content_html":"<p style=\"text-align: left;\">The interior designer earned <math alttext=\"dollar sign 68\"><mo>$</mo><mn>68</mn></math> per hour drawing up plans last week.</p>","ord":2},{"label":"D","content_html":"<p style=\"text-align: left;\">The interior designer worked <math alttext=\"68\"><mn>68</mn>\n</math> hours consulting last week.</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}}