Question

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

Answer 1

To determine the possible solutions for the number of cats (x) and dogs (y) at Parakeets Pet Store given the conditions:

1. The combined total of cats and dogs cannot exceed 20:
\[
x + y \leq 20
\]

2. The number of cats cannot exceed 8:
\[
x \leq 8
\]

Now, let’s evaluate each option provided:

1. (8, 12):
- \( 8 + 12 = 20 \leq 20 \) (satisfies)
- \( x = 8 \leq 8 \) (satisfies)
- **Valid solution.**

2. (18, 0):
- \( 18 + 0 = 18 \leq 20 \) (satisfies)
- \( x = 18 \not\leq 8 \) (does not satisfy)
- **Not valid.**

3. (12, 8):
- \( 12 + 8 = 20 \leq 20 \) (satisfies)
- \( x = 12 \not\leq 8 \) (does not satisfy)
- **Not valid.**

4. (0, 18):
- \( 0 + 18 = 18 \leq 20 \) (satisfies)
- \( x = 0 \leq 8 \) (satisfies)
- **Valid solution.**

5. (9, 11):
- \( 9 + 11 = 20 \leq 20 \) (satisfies)
- \( x = 9 \not\leq 8 \) (does not satisfy)
- **Not valid.**

6. (6, 14):
- \( 6 + 14 = 20 \leq 20 \) (satisfies)
- \( x = 6 \leq 8 \) (satisfies)
- **Valid solution.**

7. (7, 15):
- \( 7 + 15 = 22 > 20 \) (does not satisfy)
- **Not valid.**

8. (14, 6):
- \( 14 + 6 = 20 \leq 20 \) (satisfies)
- \( x = 14 \not\leq 8 \) (does not satisfy)
- **Not valid.**

Putting it all together, the valid solutions are:

- (8, 12)
- (0, 18)
- (6, 14)

So, the final possible solutions are:
- **(8, 12)**
- **(0, 18)**
- **(6, 14)**