Graphing Inequalities and Solutions

The video tutorial explains a problem involving Samuel buying doughnuts and brownies with a budget of $25. It defines variables for the number of doughnuts and brownies, sets up inequalities to represent spending limits and minimum purchase requirements, and solves these inequalities using slope-intercept form. The tutorial demonstrates graphing the inequalities to find the solution region and concludes with an example solution, encouraging further practice.

What is the total budget Samuel has for buying donuts and brownies?

• $20

• $25

• $30

• $35

How much does each donut cost?

• $1.00

• $2.50

• $1.50

• $2.00

What is the cost of each brownie?

• $1.50

• $3.00

• $2.00

• $2.50

What does the variable X represent in the problem?

• Total items

• Number of donuts

• Number of brownies

• Total cost

What does the variable Y represent in the problem?

• Number of donuts

• Number of brownies

• Total cost

• Total items

What is the first inequality representing the budget constraint?

• 1.5X + 2.5Y < 25

• 1.5X + 2.5Y = 25

• 1.5X + 2.5Y ≤ 25

• 1.5X + 2.5Y ≥ 25

What is the slope-intercept form of the first inequality?

• Y = -0.6X + 10

• Y ≥ -0.6X + 10

• Y < -0.6X + 10

• Y ≤ -0.6X + 10

What is the inequality symbol used for the budget constraint?

• <

• >

• ≤

• ≥

What operation is used to transform the inequality into slope-intercept form?

• Addition

• Subtraction

• Division

• Multiplication

What is the result of dividing 25 by 2.5 in the context of the problem?

• 15

• 5

• 10

• 20