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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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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