{"id":"cb_question_bank:aea9b7cb-4f3a-4f26-aca9-6b28f92dc517","source_id":"cb_question_bank","source_item_id":"aea9b7cb-4f3a-4f26-aca9-6b28f92dc517","external_id":null,"ibn":"05385-DC","question_id":"963da34c","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, which inequality shows the allowable width x , in inches, of the box?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The&nbsp;restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130&nbsp;inches. The perimeter of the base is determined using the width and length of the box. If&nbsp;a box has a height of 60&nbsp;inches and its length is 2.5&nbsp;times the width, which inequality shows the allowable width <span class=\"italic\">x</span>, in inches, of the box?</p>\n","rationale_html":"<p>Choice A is correct. If <span class=\"italic\">x</span> is the width, in inches, of the box, then the length of the box is 2.5<span class=\"italic\">x</span> inches. It follows that the perimeter of the base is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b53c8095c9e009a5b0aec5292a5b7e60458667f8f4b18cc64c70768baa168134\" alt=\"2 times, open parenthesis, 2 point 5 x plus x, close parenthesis\"></span>, or 7<span class=\"italic\">x</span> inches. The height of the box is given to be 60 inches. According to the restriction, the sum of the perimeter of the base and the height of the box should not exceed 130 inches. Algebraically, this can be represented by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0a3789551fe639e165a19272ee21fed038b33a2af3a7e5d86b00788d76686899\" alt=\"7 x plus 60, is less than or equal to 130\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/73c2a25e8fde9a21b9dd5bdeca33ca3b909b453f6b949d654380a4f64556a3f9\" alt=\"7 x is less than or equal to 70\"></span>. Dividing both sides of the inequality by 7 gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6f968393e08c02bcc2c63d3fa9ee284e5ba0aa366678f835d59a5a370da39f5b\" alt=\"x is less than or equal to 10\"></span>. Since <span class=\"italic\">x</span> represents the width of the box, <span class=\"italic\">x</span> must also be a positive number. Therefore, the inequality <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/47d98d43672b8fb73774f8a4e414a60815fb631366415ade9b2a8298ca8ca5bd\" alt=\"0 is less than x, which is less than or equal to 10\"></span> represents all the allowable values of <span class=\"italic\">x</span> that satisfy the given conditions.</p><p>Choices B, C, and D are incorrect and may result from calculation errors or misreading the given information.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.629000+00:00","source_updated_at":"2023-08-02T20:25:59.629000+00:00","options":[{"label":"A","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/47d98d43672b8fb73774f8a4e414a60815fb631366415ade9b2a8298ca8ca5bd\" alt=\"zero is less than x, which is less than or equal to 10\"></span>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5dafad1cc0aa525c12800ad4d0ceb61bc26fb87244988894f3453cadcc768302\" alt=\"zero is less than x, which is less than or equal to 11 and two-thirds\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/02783fa65f4397f9601b9172bb094f1e993046216400d9808d66667ca319deab\" alt=\"zero is less than x, which is less than or equal to 17 and one-half\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/201ee3d3e31fea36b73540316b19372540cc4f4cd5ad2067938af21c1310a0e3\" alt=\"zero is less than x, which is less than or equal to 20\"></span></span>\n          </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}}