Solving Complex Systems of Linear Inequalities

The video tutorial explains how Luis plans to cook meals for at least 20 people with a budget of no more than $100. It defines variables for vegetarian and meat meals, sets up inequalities based on constraints, and guides through solving these inequalities to find the correct system that represents the problem. The tutorial emphasizes understanding each constraint and using deductive reasoning to eliminate incorrect options.

What are the variables defined in Luis's meal planning problem?

• x is the number of meals with meat, y is the number of vegetarian meals

• x is the number of vegetarian meals, y is the number of meals with meat

• x is the total cost, y is the total number of meals

• x is the number of people, y is the budget

What is the minimum total number of meals Luis needs to cook?

• 20

• 15

• 25

• 10

Which inequality represents the constraint on the total number of meals?

• x + y ≤ 20

• x + y ≥ 20

• x + y = 20

• x + y < 20

What is the cost of each vegetarian meal?

• $4.00

• $2.50

• $3.00

• $4.50

What is the cost of each meal with meat?

• $4.50

• $3.00

• $4.00

• $3.50

What is the maximum budget Luis has for the meals?

• $100

• $90

• $110

• $80

Which inequality represents the budget constraint?

• 3x + 4.5y ≤ 100

• 3x + 4.5y ≥ 100

• 3x + 4.5y = 100

• 3x + 4.5y < 100

What is the minimum number of vegetarian meals Luis wants to cook?

• 6

• 5

• 7

• 4

What is the minimum number of meals with meat Luis wants to cook?

• 7

• 6

• 5

• 4

Which choice correctly represents all the constraints given in the problem?

• Choice D

• Choice C

• Choice B

• Choice A