{"id":"cb_question_bank:0f19277e-0678-408d-9177-8b708072d7a4","source_id":"cb_question_bank","source_item_id":"0f19277e-0678-408d-9177-8b708072d7a4","external_id":"d70b4faa-5ce1-4664-ae31-432dc125273a","ibn":null,"question_id":"be9cb6a2","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The cost of renting a backhoe for up to 10 days is dollar sign 270 for the first day and dollar sign 135 for each additional day. Which of the following equations gives the cost y , in dollars, of renting the backhoe for x days, where x is a positive integer and x less than or equals 10 ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The cost of renting a backhoe for up to <math alttext=\"10\"><mn>10</mn>\n</math> days is <math alttext=\"dollar sign 270\"><mo>$</mo><mn>270</mn>\n</math> for the first day and <math alttext=\"dollar sign 135\"><mo>$</mo><mn>135</mn>\n</math> for each additional day. Which of the following equations gives the cost <math alttext=\"y\"><mi>y</mi>\n</math>, in dollars, of renting the backhoe for <math alttext=\"x\"><mi>x</mi>\n</math> days, where <math alttext=\"x\"><mi>x</mi>\n</math> is a positive integer and <math alttext=\"x less than or equals 10\"><mi>x</mi><mo>≤</mo><mn>10</mn></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. It's given that the cost of renting a backhoe for up to <math alttext=\"10\"><mn>10</mn>\n</math> days is <math alttext=\"dollar sign 270\"><mo>$</mo><mn>270</mn>\n</math> for the first day and <math alttext=\"dollar sign 135\"><mo>$</mo><mn>135</mn>\n</math> for each additional day. Therefore, the cost <math alttext=\"y\"><mi>y</mi>\n</math>, in dollars, for <math alttext=\"x\"><mi>x</mi>\n</math> days, where <math alttext=\"x less than or equals 10\"><mi>x</mi><mo>≤</mo><mn>10</mn></math>, is the sum of the cost for the first day, <math alttext=\"dollar sign 270\"><mo>$</mo><mn>270</mn>\n</math>, and the cost for the additional <math alttext=\"x minus 1\"><mrow>\n\t<mi>x</mi>\n\t<mo>-</mo>\n\t<mn>1</mn>\n</mrow>\n</math> days, <math alttext=\"dollar sign 135 left parenthesis x minus 1 right parenthesis\"><mo>$</mo><mn>135</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math>. It follows that <math alttext=\"y equals 270 plus 135 left parenthesis x minus 1 right parenthesis\"><mi>y</mi><mo>=</mo><mn>270</mn><mo>+</mo><mn>135</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math>, which is equivalent to <math alttext=\"y equals 270 plus 135 x minus 135\"><mi>y</mi><mo>=</mo><mn>270</mn><mo>+</mo><mn>135</mn><mi>x</mi><mo>-</mo><mn>135</mn></math>, or&nbsp;<math alttext=\"y equals 135 x plus 135\"><mi>y</mi><mo>=</mo><mn>135</mn><mi>x</mi><mo>+</mo><mn>135</mn></math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This equation represents a situation where the cost of renting a backhoe is <math alttext=\"dollar sign 135\"><mo>$</mo><mn>135</mn>\n</math> for the first day and <math alttext=\"dollar sign 270\"><mo>$</mo><mn>270</mn>\n</math> for each additional day.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.810000+00:00","source_updated_at":"2023-08-02T20:25:59.810000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"y equals 270 x minus 135\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>270</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>-</mo>\n\t\t<mn>135</mn>\n\t</mrow>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"y equals 270 x plus 135\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>270</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>135</mn>\n\t</mrow>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"y equals 135 x plus 270\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>135</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>270</mn>\n\t</mrow>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"y equals 135 x plus 135\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>135</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>135</mn>\n\t</mrow>\n</mrow>\n</math></p>","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}}