{"id":"cb_question_bank:e5efadfb-b666-4f20-a789-65a3a8acfccb","source_id":"cb_question_bank","source_item_id":"e5efadfb-b666-4f20-a789-65a3a8acfccb","external_id":null,"ibn":"070614-DC","question_id":"a1fd2304","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":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"How many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to obtain a 15% saline solution?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">How many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to obtain a 15% saline solution?</p>\n","rationale_html":"<p>The correct answer is 1.5. The total amount, in liters, of a saline solution can be expressed as the liters of each type of saline solution multiplied by the percent concentration of the saline solution. This gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/09a402dc648c40148f9fae694bbf71b3cd6cdb248bfff4c5838d6a62214cf39e\" alt=\"3 times 0 point 1 0\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8d1e9533625aff63d8d30ec718a355970ff3200c97324bc12379b25583e8b5f0\" alt=\"x times 0 point 2 5\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3482b95b7bc24c991d3b427ab5f407a558499cd69d4d89da3c26f03690676807\" alt=\"open parenthesis, x plus 3, close parenthesis, times, open parenthesis, 0 point 1 5, close parenthesis\"></span>, where <span class=\"italic\">x</span> is the amount, in liters, of 25% saline solution and 10%, 15%, and 25% are represented as 0.10, 0.15, and 0.25, respectively. Thus, the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d547e29c4003bd548049cd5e3876e522c432b0ab917edbc29c0c16783c2a266e\" alt=\"3 times 0 point 1 0, plus 0 point 2 5 x, equals, 0 point 1 5 times, open parenthesis, x plus 3, close parenthesis\"></span> must be true. Multiplying 3 by 0.10 and distributing 0.15 to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/09d35da799589b5895190e23c45b5134bc9632c6489ac82d2fdf3dda1a9ede48\" alt=\"open parenthesis, x plus 3, close parenthesis\"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/aa0dcac6d74459723b501e9f9a13b347b2c68fbf8dab61ed37780e116430d4e5\" alt=\"0 point 3 0, plus 0 point 2 5 x, equals, 0 point 1 5 x, plus 0 point 4 5\"></span>. Subtracting 0.15<span class=\"italic\">x</span> and 0.30 from each side of the equation gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6ec25c0d111fdc6e32795dc6759f32304debdbeff6896d0f2cfd4825265ef30a\" alt=\"0 point 1 0 x, equals 0 point 1 5\"></span>. Dividing each side of the equation by 0.10 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4bb4a6738c3dc24b0df3735de67b04ae28628da434347d0ee2679b4526aef321\" alt=\"x equals 1 point 5\"></span>. Note that 1.5 and 3/2 are examples of ways to enter a correct answer.</p>\n","correct_answer":["1.5"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.631000+00:00","source_updated_at":"2023-08-02T20:25:59.631000+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}}