{"id":"cb_question_bank:fb74942b-cd3e-4a8a-938d-7df8674c4ed5","source_id":"cb_question_bank","source_item_id":"fb74942b-cd3e-4a8a-938d-7df8674c4ed5","external_id":"9040ee10-4498-4a27-b92f-5181148b3e11","ibn":null,"question_id":"535fa6e6","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in 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":"Davio bought some potatoes and celery. The potatoes cost dollar sign 0.69 per pound, and the celery cost dollar sign 0.99 per pound. If Davio spent dollar sign 5.34 in total and bought twice as many pounds of celery as pounds of potatoes, how many pounds of celery did Davio buy?","stimulus":"","stimulus_html":null,"stem_html":"<p>Davio bought some potatoes and celery. The potatoes cost <math alttext=\"dollar sign 0.69\"><mo>$</mo><mn>0.69</mn></math> per pound, and the celery cost <math alttext=\"dollar sign 0.99\"><mo>$</mo><mn>0.99</mn></math> per pound. If Davio spent <math alttext=\"dollar sign 5.34\"><mo>$</mo><mn>5.34</mn></math> in total and bought twice as many pounds of celery as pounds of potatoes, how many pounds of celery did Davio buy?</p>","rationale_html":"<p>Choice D is correct. Let <math alttext=\"p\"><mi>p</mi></math> represent the number of pounds of potatoes and let <math alttext=\"c\"><mi>c</mi></math> represent the number of pounds of celery&nbsp;that Davio bought. It’s given that potatoes cost <math alttext=\"dollar sign 0.69\"><mo>$</mo><mn>0.69</mn></math> per pound and celery costs <math alttext=\"dollar sign 0.99\"><mo>$</mo><mn>0.99</mn></math> per pound. If Davio spent <math alttext=\"dollar sign 5.34\"><mo>$</mo><mn>5.34</mn></math> in total, then the equation <math alttext=\"0.69 p plus 0.99 c equals 5.34\"><mn>0.69</mn><mi>p</mi><mo>+</mo><mn>0.99</mn><mi>c</mi><mo>=</mo><mn>5.34</mn></math> represents this situation. It’s also given that Davio bought twice as many pounds of celery as pounds of potatoes; therefore, <math alttext=\"c equals 2 p\"><mi>c</mi><mo>=</mo><mn>2</mn><mi>p</mi></math>. Substituting <math alttext=\"2 p\"><mn>2</mn><mi>p</mi></math> for <math alttext=\"c\"><mi>c</mi></math> in the equation <math alttext=\"0.69 p plus 0.99 c equals 5.34\"><mn>0.69</mn><mi>p</mi><mo>+</mo><mn>0.99</mn><mi>c</mi><mo>=</mo><mn>5.34</mn></math> yields <math alttext=\"0.69 p plus 0.99 left parenthesis 2 p right parenthesis equals 5.34\"><mn>0.69</mn><mi>p</mi><mo>+</mo><mn>0.99</mn><mfenced><mrow><mn>2</mn><mi>p</mi></mrow></mfenced><mo>=</mo><mn>5.34</mn></math>, which is equivalent to <math alttext=\"0.69 p plus 1.98 p equals 5.34\"><mn>0.69</mn><mi>p</mi><mo>+</mo><mn>1.98</mn><mi>p</mi><mo>=</mo><mn>5.34</mn></math>, or <math alttext=\"2.67 p equals 5.34\"><mn>2.67</mn><mi>p</mi><mo>=</mo><mn>5.34</mn></math>. Dividing both sides of this equation by <math alttext=\"2.67\"><mn>2.67</mn></math> yields <math alttext=\"p equals 2\"><mi>p</mi><mo>=</mo><mn>2</mn></math>. Substituting&nbsp;<math alttext=\"2\"><mn>2</mn></math> for&nbsp;<math alttext=\"p\"><mi>p</mi></math> in the equation&nbsp;<math alttext=\"c equals 2 p\"><mi>c</mi><mo>=</mo><mn>2</mn><mi>p</mi></math> yields&nbsp;<math alttext=\"c equals 2 left parenthesis 2 right parenthesis\"><mi>c</mi><mo>=</mo><mn>2</mn><mfenced><mn>2</mn></mfenced></math>, or&nbsp;<math alttext=\"c equals 4\"><mi>c</mi><mo>=</mo><mn>4</mn></math>. Therefore, Davio bought&nbsp;<math alttext=\"4\"><mn>4</mn></math> pounds of celery.</p>\n<p>Choice A is incorrect. This is the number of pounds of potatoes, not the number of pounds of celery, Davio bought.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>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":"2023-08-02T20:25:59.813000+00:00","source_updated_at":"2023-08-02T20:25:59.813000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"2\"><mn>2</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"2.5\"><mn>2.5</mn></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"2.67\"><mn>2.67</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"4\"><mn>4</mn>\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}}