{"id":"cb_question_bank:c908b48f-b01d-49f8-80cd-2b388e02e8b7","source_id":"cb_question_bank","source_item_id":"c908b48f-b01d-49f8-80cd-2b388e02e8b7","external_id":null,"ibn":"05043-DC","question_id":"36ab4122","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Megan’s regular wage at her job is p dollars per hour for the first 8 hours of work in a day plus 1.5 times her regular hourly wage for work in excess of 8 hours that day. On a given day, Megan worked for 10 hours, and her total earnings for that day were $137.50. What is Megan’s regular hourly wage?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Megan’s regular wage at her job is <em class=\"inline_variable \">p</em>&nbsp;dollars per hour for the first 8 hours of work in a day plus 1.5&nbsp;times her regular hourly wage for work in excess of 8&nbsp;hours that day. On a given day, Megan worked for 10&nbsp;hours, and her total earnings for that day were&nbsp;$137.50. What is Megan’s regular hourly wage?</p>\n","rationale_html":"<p>Choice B is correct. Since <span class=\"italic\">p</span> represents Megan’s regular pay per hour, 1.5<span class=\"italic\">p</span> represents the pay per hour in excess of 8 hours. Since Megan worked for 10 hours, she must have been paid <span class=\"italic\">p</span> dollars per hour for 8 of the hours plus 1.5<span class=\"italic\">p</span> dollars per hour for the remaining 2 hours. Therefore, since Megan earned $137.50 for the 10 hours, the situation can be represented by the equation 137.5 = 8<span class=\"italic\">p</span> + 2(1.5)<span class=\"italic\">p.&nbsp;</span>Distributing the 2 in the equation gives 137.5 = 8<span class=\"italic\">p</span> + 3<span class=\"italic\">p</span>, and combining like terms gives 137.5 = 11<span class=\"italic\">p</span>. Dividing both sides by 11 gives <span class=\"italic\">p</span> = 12.5. Therefore, Megan’s regular wage is $12.50.</p><p>Choices A and C are incorrect and may be the result of&nbsp;calculation errors. Choice D is incorrect and may result from finding the average hourly wage that Megan earned for the 10 hours of work.</p><p></p>\n","correct_answer":["B"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.628000+00:00","source_updated_at":"2023-08-02T20:25:59.628000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">$11.75</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">$12.50</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">$13.25</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">$13.75</p>\n","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}}