{"id":"cb_question_bank:b77ba45d-6acc-4b11-b5f2-81b7b6546fd9","source_id":"cb_question_bank","source_item_id":"b77ba45d-6acc-4b11-b5f2-81b7b6546fd9","external_id":"bc24a37b-b601-44de-a222-60974e9db0fb","ibn":null,"question_id":"1e11190a","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Store A sells raspberries for dollar sign 5.50 per pint and blackberries for dollar sign 3.00 per pint. Store B sells raspberries for dollar sign 6.50 per pint and blackberries for dollar sign 8.00 per pint. A certain purchase of raspberries and blackberries would cost dollar sign 37.00 at Store A or dollar sign 66.00 at Store B. How many pints of blackberries are in this purchase?","stimulus":"","stimulus_html":null,"stem_html":"

Store A sells raspberries for $5.50\n per pint and blackberries for $3.00\n per pint. Store B sells raspberries for $6.50\n per pint and blackberries for $8.00\n per pint. A certain purchase of raspberries and blackberries would cost $37.00\n at Store A or $66.00\n at Store B. How many pints of blackberries are in this purchase?

","rationale_html":"

Choice C is correct. It’s given that store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint, and a certain purchase of raspberries and blackberries at store A would cost $37.00. It’s also given that store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint, and this purchase of raspberries and blackberries at store B would cost $66.00. Let r\n represent the number of pints of raspberries and b\n represent the number of pints of blackberries in this purchase. The equation 5.50r+3.00b=37.00 represents this purchase of raspberries and blackberries from store A and the equation 6.50r+8.00b=66.00 represents this purchase of raspberries and blackberries from store B. Solving the system of equations by elimination gives the value of r\n and the value of b\n that make the system of equations true. Multiplying both sides of the equation for store A by 6.5\n yields 5.50r6.5+3.00b6.5=37.006.5, or 35.75r+19.5b=240.5. Multiplying both sides of the equation for store B by 5.5\n yields 6.50r5.5+8.00b5.5=66.005.5, or 35.75r+44b=363. Subtracting both sides of the equation for store A, 35.75r+19.5b=240.5, from the corresponding sides of the equation for store B, 35.75r+44b=363, yields 35.75r-35.75r+44b-19.5b=363-240.5, or 24.5b=122.5. Dividing both sides of this equationby 24.5\n yields b=5. Thus, 5\n pints of blackberries are in
this purchase.

\n


Choices A and B are incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is the number of pints of raspberries, not blackberries, in the purchase.

","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.816000+00:00","source_updated_at":"2023-08-02T20:25:59.816000+00:00","options":[{"label":"A","content_html":"

4\n

","ord":0},{"label":"B","content_html":"

5\n

","ord":1},{"label":"C","content_html":"

8\n

","ord":2},{"label":"D","content_html":"

12\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}}