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?
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A
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B
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C
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D
Correct answer: B
Explanation
Choice B is correct. Marisa will hire x junior directors and y senior directors. Since she needs to hire at least 10 staff members, . Each junior director will be paid $640 per week, and each senior director will be paid $880 per week. Marisa’s budget for paying the new staff is no more than $9,700 per week; in terms of x and y, this condition is
. Since Marisa must hire at least 3 junior directors and at least 1 senior director, it follows that
and
. All four of these conditions are represented correctly in choice B.
Choices A and C are incorrect. For example, the first condition, , in each of these options implies that Marisa can pay the new staff members more than her budget of $9,700. Choice D is incorrect because Marisa needs to hire at least 10 staff members, not at most 10 staff members, as the inequality
implies.
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