{"id":"cb_question_bank:28c54699-758c-492d-9adf-76245f0b9045","source_id":"cb_question_bank","source_item_id":"28c54699-758c-492d-9adf-76245f0b9045","external_id":null,"ibn":"09101-DC","question_id":"2c121b25","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or 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":"Valentina bought two containers of beads. In the first container 30% of the beads are red, and in the second container 70% of the beads are red. Together, the containers have at least 400 red beads. Which inequality shows this relationship, where x is the total number of beads in the first container and y is the total number of beads in the second container?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Valentina bought two containers of beads. In the first container 30% of the beads are red, and in the second container 70% of the beads are red. Together, the containers have at least 400 red beads. Which inequality shows this relationship, where <span class=\"italic\">x</span> is the total number of beads in the first container and <span class=\"italic\">y</span> is the total number of beads in the second container?</p>\n","rationale_html":"<p>Choice A is correct. It is given that <span class=\"italic\">x</span> is the total number of beads in the first container and that 30% of those beads are red; therefore, the expression 0.3<span class=\"italic\">x</span> represents the number of red beads in the first container. It is given that <span class=\"italic\">y</span> is the total number of beads in the second container and that 70% of those beads are red; therefore, the expression 0.7<span class=\"italic\">y</span> represents the number of red beads in the second container. It is also given that, together, the containers have at least 400 red beads, so the inequality that shows this relationship is 0.3<span class=\"italic\">x</span> + 0.7<span class=\"italic\">y</span> ≥ 400.</p><p>Choice B is incorrect because it represents the containers having a total of at most, rather than at least, 400 red beads. Choice C is incorrect and may be the result of misunderstanding how to represent a percentage of beads in each container. Also, the inequality shows the containers having a combined total of at most, rather than at least, 400 red beads. Choice D is incorrect because the percentages were not converted to decimals.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.636000+00:00","source_updated_at":"2023-08-02T20:25:59.636000+00:00","options":[{"label":"A","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/65a52eacbb855eedc5a2569826cf876052623042842e48335d3609b5992400ca\" alt=\"0 point 3 x, plus, 0 point 7 y, is greater than or equal to, 400\"></span></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a298445e8a8039389a5d2d16d84d513376ad3a1b6bb5e386b809f966568b2a16\" alt=\"0 point 7 x, plus, 0 point 3 y, is less than or equal to, 400\"></span></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ae6bdf88f9f2cc46f7661a69ca0fe6c6e69ee836617a965305a0ec3ceb72ca90\" alt=\"the fraction x over 3, end fraction, plus, the fraction y over 7, end fraction, is less than or equal to, 400\"></span></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/452b03a6265cf42da5eae904b72ad8c75eaeab506dcd5525cef9afd262bae68a\" alt=\"30 x, plus, 70 y, is greater than or equal to, 400\"></span></span>\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}}