Parakeets Pet Store never has more than a combined total of 20 cats and dogs and never more than 8 cats. Given that x represents the number of cats at the pet store and y represents the number of dogs at the pet store, SELECT ALL possible solutions.

Question

Responses
(8, 12)
(18, 0)
(12, 8)
(0, 18)
(9, 11)
(6, 14)
(7, 15)
(14, 6)

Answer 1

To determine the valid solutions for the number of cats (x) and dogs (y) at Parakeets Pet Store, we need to consider the following constraints:

1. The total number of cats and dogs cannot exceed 20:
   \( x + y \leq 20 \)

2. The number of cats cannot exceed 8:
   \( x \leq 8 \)

Now, we will evaluate each option:

1. (8, 12):

   • \( x + y = 8 + 12 = 20 \) (valid since ≤ 20)
   • \( x = 8 \) (valid since ≤ 8)
   • Valid.

2. (18, 0):

   • \( x + y = 18 + 0 = 18 \) (valid since ≤ 20)
   • \( x = 18 \) (invalid since > 8)
   • Not Valid.

3. (12, 8):

   • \( x + y = 12 + 8 = 20 \) (valid since ≤ 20)
   • \( x = 12 \) (invalid since > 8)
   • Not Valid.

4. (0, 18):

   • \( x + y = 0 + 18 = 18 \) (valid since ≤ 20)
   • \( x = 0 \) (valid since ≤ 8)
   • Valid.

5. (9, 11):

   • \( x + y = 9 + 11 = 20 \) (valid since ≤ 20)
   • \( x = 9 \) (invalid since > 8)
   • Not Valid.

6. (6, 14):

   • \( x + y = 6 + 14 = 20 \) (valid since ≤ 20)
   • \( x = 6 \) (valid since ≤ 8)
   • Valid.

7. (7, 15):

   • \( x + y = 7 + 15 = 22 \) (invalid since > 20)
   • Not Valid.

8. (14, 6):

   • \( x + y = 14 + 6 = 20 \) (valid since ≤ 20)
   • \( x = 14 \) (invalid since > 8)
   • Not Valid.

Final Valid Solutions:

• (8, 12)
• (0, 18)
• (6, 14)

Thus, the valid responses based on the constraints provided are:

• (8, 12)
• (0, 18)
• (6, 14)