{"id":"cb_question_bank:bd5c0a67-f9cd-4ba7-814e-9d308088f9cb","source_id":"cb_question_bank","source_item_id":"bd5c0a67-f9cd-4ba7-814e-9d308088f9cb","external_id":null,"ibn":"05355-DC","question_id":"b8e73b5b","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":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for the week?","stimulus":"","stimulus_html":null,"stem_html":"

Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for the week?

\n","rationale_html":"

Choice C is correct. Ken earned $8 per hour for the first 10 hours he worked, so he earned a total of $80 for the first 10 hours he worked. For the rest of the week, Ken was paid at the rate of $10 per hour. Let x be the number of hours he will work for the rest of the week. The total of Ken’s earnings, in dollars, for the week will be \"10. He saves 90% of his earnings each week, so this week he will save \"0 dollars. The inequality \"0 represents the condition that he will save at least $270 for the week. Factoring 10 out of the expression \"10 gives \"10. The product of 10 and 0.9 is 9, so the inequality can be rewritten as \"9. Dividing both sides of this inequality by 9 yields \"x, so \"x. Therefore, the least number of hours Ken must work the rest of the week to save at least $270 for the week is 22.

Choices A and B are incorrect because Ken can save $270 by working fewer hours than 38 or 33 for the rest of the week. Choice D is incorrect. If Ken worked 16 hours for the rest of the week, his total earnings for the week will be \"80, which is less than $270. Since he saves only 90% of his earnings each week, he would save even less than $240 for the week.

\n","correct_answer":["C"],"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":"

38

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

33

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

22

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

16

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