Answer:
One possible solution that satisfies all the conditions is Andrew working 9 hours lifeguarding and 6 hours washing cars.
Step-by-step explanation:
Andrew's situation can be represented by the following system of inequalities:
Let x represent the number of hours lifeguarding and y represent the number of hours washing cars.
The inequalities can be written as:
1. x ≥ 9 (He must work at least 9 hours lifeguarding)
2. y ≤ 3 (He can work at most 3 hours washing cars)
3. x + y ≤ 15 (He can work at most 15 total hours)
4. 14x + 10y ≥ 170 (He must earn no less than $170)
Now let's graph these inequalities to find a possible solution:
- First, graph the line x = 9 (vertical line passing through x = 9).
- Then graph the line y = 3 (horizontal line passing through y = 3).
- Next, graph the line x + y = 15 (diagonal line where x + y equals 15).
- Finally, graph the line 14x + 10y = 170 (the line representing earnings of at least $170).
The intersection of these shaded regions represents the feasible area where all conditions are satisfied.
From the graph, the feasible region appears to be a triangular area. The vertices of the feasible region are the points where the lines intersect:
- (9, 3)
- (9, 6)
- (11, 4)
Let's check one of these points to determine a possible solution. Let's take (9, 6):
- Lifeguarding hours (x): 9 hours
- Washing cars hours (y): 6 hours
Total hours worked: x + y = 9 + 6 = 15 (within the limit)
Earnings: 14x + 10y = 14(9) + 10(6) = 126 + 60 = 186 (more than $170)
Therefore, one possible solution that satisfies all the conditions is Andrew working 9 hours lifeguarding and 6 hours washing cars.