Exploring Systems of Inequalities through Word Problems

The video tutorial covers solving systems of inequalities graphically. It begins with an introduction to the topic, followed by two real-world examples. The first example involves Sarah's jewelry business, where students learn to find a solution set for maximizing profit under constraints. The second example involves Jason's party planning, focusing on purchasing within a budget. The tutorial emphasizes graphing techniques, identifying solution sets, and verifying solutions.

What is the maximum number of orders Sarah can make?

• 200

• 250

• 300

• 450

In the context of Sarah's sales, what does the inequality X + Y ≤ 250 represent?

• The total number of bracelets and earrings she can make

• The minimum number of orders she needs to make

• The total cost of bracelets and earrings

• The total profit from selling bracelets and earrings

What is the y-intercept of the inequality Y ≤ -X + 250?

• 150

• 0

• 200

• 250

When graphing the inequality 2X + 3Y > 450, what type of line should be used?

• Double line

• Solid line

• Dotted line

• Dashed line

Which point is a solution to the system of inequalities for Sarah's sales?

• (50, 200)

• (100, 100)

• (150, 50)

• (200, 50)

What is the cost of one package of wings in Jason's example?

• $10

• $7

• $6

• $4

In Jason's example, what does the inequality X + Y ≥ 6 represent?

• The total number of wings and hot dogs he can buy

• The minimum number of packages he needs to buy

• The total cost of wings and hot dogs

• The maximum number of packages he can buy

What is the y-intercept of the inequality Y ≤ -7/4X + 15?

• 0

• 60

• 6

• 15

Which point is a solution to the system of inequalities for Jason's purchases?

• (5, 7)

• (4, 6)

• (3, 5)

• (2, 10)

What is the maximum amount Jason can spend on wings and hot dogs?

• $55

• $65

• $50

• $60