{"id":"cb_question_bank:7b9d35b1-3474-4f4c-91eb-be3dcec61b33","source_id":"cb_question_bank","source_item_id":"7b9d35b1-3474-4f4c-91eb-be3dcec61b33","external_id":null,"ibn":"05268-DC","question_id":"d7bf55e1","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A movie theater sells two types of tickets, adult tickets for $12 and child tickets for $8. If the theater sold 30 tickets for a total of $300, how much, in dollars, was spent on adult tickets? (Disregard the $ sign when gridding your answer.)","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A movie theater sells two types of tickets, adult tickets for $12 and child tickets for $8. If the theater sold 30&nbsp;tickets for a total&nbsp;of $300, how much, in dollars, was spent on adult tickets? (Disregard the $ sign when gridding your answer.)</p>\n","rationale_html":"<p>The correct answer is 180. Let <span class=\"italic\">a</span> be the number of adult tickets sold and <span class=\"italic\">c</span> be the number of child tickets sold. Since the theater sold a total of 30 tickets, <span class=\"italic\">a</span> + <span class=\"italic\">c</span> = 30. The price per adult ticket is $12, and the price per child ticket is $8. Since the theater received a total of $300 for the 30 tickets sold, it follows that 12<span class=\"italic\">a</span> + 8<span class=\"italic\">c</span> = 300. To eliminate <span class=\"italic\">c</span>, the first equation can be multiplied by 8 and then subtracted from the second equation:<br>\n&nbsp; <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c667eaa553905262b5c5a5753e9779847b11d09e47d0cab438bc500e38b62275\" alt=\"12 a, plus 8 c, equals 300, and negative 8 a, minus 8 c, equals negative 240, gives 4 a, plus 0 c, equals 60\"></span></p><p>Because the question asks for the amount spent on adult tickets, which is 12<span class=\"italic\">a</span> dollars, the resulting equation can be multiplied by 3 to give 3(4<span class=\"italic\">a</span>) = 3(60) = 180. Therefore, $180 was spent on adult tickets.</p><p>Alternate approach: If all the 30 tickets sold were child tickets, their total price would be 30($8) = $240. Since the actual total price of the 30 tickets was $300, the extra $60 indicates that a certain number of adult tickets, <span class=\"italic\">a</span>, were sold. Since the price of each adult ticket is $4 more than each child ticket, 4<span class=\"italic\">a</span> = 60, and it follows that 12<span class=\"italic\">a</span> = 180.</p><p></p>\n","correct_answer":["180"],"has_media":true,"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":[],"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}}