Final answer:
The system of inequalities to model the situation is x + y ≤ 20 and x ≤ 8. By graphing, we find the feasible region considering x, y ≥ 0. Reasonable solutions include the ordered pairs (3, 17), (8, 12), and (5, 15).
Step-by-step explanation:
To model the situation described, we can use two variables: let x be the number of cats and y be the number of dogs in Renee's pet store. The system of inequalities based on the information given would be:
- x + y ≤ 20
- x ≤ 8
- y ≥ 0
- x ≥ 0
Solving this system through graphing involves plotting these inequalities on a coordinate plane:
- The line x + y = 20 represents the boundary where the sum of cats and dogs is 20. We shade below this line because the pet store can have at most 20 cats and dogs combined.
- The line x = 8 represents the boundary for the maximum number of cats. We shade to the left of this line, indicating that the number of cats is no more than 8.
- Since the number of cats and dogs cannot be negative, we are limited to the first quadrant where x and y are both nonnegative.
The feasible region is where all shaded areas overlap.
Three reasonable solutions as ordered pairs could be:
- (3, 17) - 3 cats and 17 dogs
- (8, 12) - 8 cats and 12 dogs
- (5, 15) - 5 cats and 15 dogs