{"id":"cb_question_bank:0a647aa0-56ae-4cc8-98c4-46202a5fa970","source_id":"cb_question_bank","source_item_id":"0a647aa0-56ae-4cc8-98c4-46202a5fa970","external_id":null,"ibn":"025812-DC","question_id":"2b15d65f","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"An economist modeled the demand Q for a certain product as a linear function of the selling price P . The demand was 20,000 units when the selling price was $40 per unit, and the demand was 15,000 units when the selling price was $60 per unit. Based on the model, what is the demand, in units, when the selling price is $55 per unit?","stimulus":"","stimulus_html":null,"stem_html":"

An economist modeled the demand Q for a certain product as a linear function of the selling price P. The demand was 20,000 units when the selling price was $40 per unit, and the demand was 15,000 units when the selling price was $60 per unit. Based on the model, what is the demand, in units, when the selling price is $55 per unit?

\n","rationale_html":"

Choice A is correct. Let the economist’s model be the linear function \"Q, where Q is the demand, P is the selling price, m is the slope of the line, and b is the y-coordinate of the y-intercept of the line in the xy-plane, where \"y. Two pairs of the selling price P and the demand Q are given. Using the coordinate pairs \"P, two points that satisfy the function are \"40 and \"60. The slope m of the function can be found using the formula \"m. Substituting the given values into this formula yields \"m, or  \"m. Therefore, \"Q. The value of b can be found by substituting one of the points into the function. Substituting the values of P and Q from the point \"with yields \"20,000, or \"20,000. Adding 10,000 to both sides of this equation yields \"b. Therefore, the linear function the economist used as the model is \"Q. Substituting 55 for P yields \"Q. It follows that when the selling price is $55 per unit, the demand is 16,250 units.

Choices B, C, and D are incorrect and may result from calculation or conceptual errors.

 

\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.620000+00:00","source_updated_at":"2023-08-02T20:25:59.620000+00:00","options":[{"label":"A","content_html":"

16,250

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

16,500

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

16,750

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

17,500

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