- Define variables: Let x be hours spent dog-walking, y be hours spent washing cars.
- Write constraints:
- Total hours: x + y ≤ 20
- Minimum earnings: 6x + 10y ≥ 150
- Non-negativity: x ≥ 0, y ≥ 0
- Graph the inequalities:
- Line x + y = 20 passes through (20, 0) and (0, 20); shade below.
- Line 6x + 10y = 150 passes through (25, 0) and (0, 15); shade above.
- Find feasible region: The shaded area where all constraints overlap.
- Verify solution: For x=6, y=12:
- Hours: 6 + 12 = 18 ≤ 20 ✓
- Earnings: 6(6) + 10(12) = 36 + 120 = 156 ≥ 150 ✓
- Conclusion: Bobbi can work 6 hours dog-walking and 12 hours washing cars to meet her goals.
Parent Tip: Review the logic above to help your child master the concept of systems of linear inequalities word problems worksheet.
