Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640 per week, and senior directors, who will be paid $880 per week. Her budget for paying the staff members is no more than $9,700 per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?
Correct answer: B. 640x + 880y ≤ 9,700x + y ≥ 10x ≥ 3y ≥ 1
- A. 640x + 880y ≥ 9,700x + y ≤ 10x ≥ 3y ≥ 1
- B. 640x + 880y ≤ 9,700x + y ≥ 10x ≥ 3y ≥ 1
- C. 640x + 880y ≥ 9,700x + y ≥ 10x ≤ 3y ≤ 1
- D. 640x + 880y ≤ 9,700x + y ≤ 10x ≤ 3y ≤ 1
Explanation
The correct answer is Option B. It correctly captures all the conditions of the problem. The inequality 640x + 880y ≤ 9,700 ensures the total weekly payment does not exceed the budget. The inequality x + y ≥ 10 ensures Marisa hires at least 10 staff members. The conditions x ≥ 3 and y ≥ 1 ensure Marisa hires at least 3 junior directors and 1 senior director. Options A, C, and D either misrepresent the budget constraint or the minimum hiring requirements.
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