Modeling Real-World Problems with Systems of Inequalities

What is the maximum number of hours John can work in a week?

• 30 hours

• 52 hours

• 60 hours

• 40 hours

How much does John need to earn per week to cover his living expenses?

• $700

• $500

• $400

• $600

Which system of inequalities represents the constraints on John's working hours and earnings?

• x + y ≤ 52, 10x + 15y ≥ 600

• x - y ≤ 52, 10x - 15y ≥ 600

• x + y ≥ 52, 10x + 15y ≤ 600

• x + y = 52, 10x + 15y = 600

What does the shaded region on the graph represent in John's context?

• Only possible earnings

• Feasible working hours and earnings

• Only possible working hours

• Impossible working hours and earnings

If John works 36 hours at the landscaping business, how many hours can he work at the bakery to meet his financial needs?

• 16 hours

• 15 hours

• 14 hours

• 13 hours

What is the minimum number of hours John must work at his father's landscaping business?

• 15 hours

• 20 hours

• 5 hours

• 10 hours

How much does John earn from 42 hours of work at the bakery?

• $610

• $560

• $520

• $630

What is the maximum number of hours John can work at the bakery if he works 10 hours at the landscaping business?

• 42 hours

• 40 hours

• 35 hours

• 45 hours

What is the total income John can generate if he works 10 hours at the landscaping business and 42 hours at the bakery?

• $720

• $700

• $750

• $730

What does the intersection of the lines on the graph represent in the context of John's work scenario?

• Maximum possible hours and earnings

• Minimum required hours and earnings

• Non-feasible working and earning scenario

• Optional working and earning scenario