Graphing and Analyzing Systems of Inequalities

Quiz
•
English, Mathematics
•
8th Grade
•
Hard
Anthony Clark
FREE Resource
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A farmer has 100 meters of fencing to create a rectangular pen for animals. If the length of the pen is represented by x and the width by y, write a system of inequalities to represent the constraints on the dimensions of the pen. What is the feasible region for the dimensions?
The system of inequalities is: {x + y ≤ 50, x ≥ 0, y ≥ 0}. The feasible region is the area in the first quadrant bounded by the line x + y = 50 and the axes.
x + y = 50
x + y ≥ 100
x ≤ 0, y ≤ 0
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A school is planning a field trip and has a budget of $500. Each student ticket costs $15 and each adult ticket costs $20. Write a system of inequalities to represent the number of student (x) and adult (y) tickets that can be purchased. What is the feasible region for ticket purchases?
10x + 15y ≤ 500, x ≥ 0, y ≥ 0
20x + 15y ≤ 500, x ≥ 0, y ≥ 0
15x + 25y ≤ 500, x ≥ 0, y ≥ 0
15x + 20y ≤ 500, x ≥ 0, y ≥ 0
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A bakery sells two types of cookies: chocolate chip and oatmeal raisin. The bakery can make a maximum of 200 cookies in a day. If the number of chocolate chip cookies is represented by x and oatmeal raisin cookies by y, write a system of inequalities to represent the production limits. What does the feasible region look like?
x + y = 200, x ≥ 0, y ≤ 0
x + y < 200, x > 0, y > 0
x + y ≥ 200, x ≤ 0, y ≤ 0
The system of inequalities is: x + y ≤ 200, x ≥ 0, y ≥ 0.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A gym has a maximum capacity of 150 members. If the number of adult members is represented by x and the number of child members by y, write a system of inequalities to represent the membership limits. How can you graphically analyze the solutions?
x + y < 150, x > 0, y > 0
x + y = 150, x < 0, y < 0
x + y ≥ 150, x ≤ 0, y ≤ 0
x + y ≤ 150, x ≥ 0, y ≥ 0
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A concert venue can accommodate a maximum of 300 people. If tickets for adults cost $25 and tickets for children cost $10, and the total revenue must be at least $5000, write a system of inequalities to represent the situation. What is the feasible region for ticket sales?
x + y >= 300, 25x + 10y <= 5000
x + y <= 300, 25x + 10y = 5000
x + y <= 300, 25x + 10y >= 5000
x + y <= 250, 25x + 10y >= 6000
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A local charity is organizing a food drive and has a goal to collect at least 300 cans of food. If they collect 5 cans for every adult volunteer (x) and 3 cans for every child volunteer (y), write a system of inequalities to represent the collection goal. How can you analyze the solutions graphically?
10x + 2y ≥ 300
2x + 4y ≥ 300
5x + 3y ≥ 300
5x + 3y < 300
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A company produces two products, A and B. Each product A requires 2 hours of labor and each product B requires 3 hours of labor. If the company has 60 hours of labor available, write a system of inequalities to represent the production limits. What does the feasible region indicate?
2x + 3y ≥ 60, x ≤ 0, y ≤ 0
2x + 3y ≤ 60, x ≥ 0, y ≥ 0
x + y ≤ 20, x ≥ 0, y ≥ 0
3x + 2y ≤ 60, x ≥ 0, y ≤ 0
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