Question Bank / Math / Linear Inequalities
Linear inequalities in one or two variables SAT question
Math · Algebra · Medium · Answer it here, explanation included.
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?
ExplanationShow
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.
Drill this skill on Aceit
Adaptive practice, a daily plan, and score tracking take a free account so we can save your work.
More Linear inequalities in one or two variables questions
- A cargo helicopter delivers only 100-pound packages and 120-pound packages. For each delivery trip, the helicopter must carry at least 10 packages, and the total weight of the pack
- The point (8,2) in the xy-plane is a solution to which of the following systems of inequalities?
- Adam's school is a 20-minute walk or a 5-minute bus ride away from his house. The bus runs once every 30 minutes, and the number of minutes, w, that Adam waits for the bus varies b
- Valentina bought two containers of beads. In the first container 30% of the beads are red, and in the second container 70% of the beads are red. Together, the containers have at le
- The total cost, in dollars, to rent a surfboard consists of a $25 service fee and a $10 per hour rental fee. A person rents a surfboard for t hours and intends to spend a maximu
- In North America, the standard width of a parking space is at least 7.5 feet and no more than 9.0 feet. A restaurant owner recently resurfaced the restaurant's parking lot and want