Question

pawsome 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, which graph represents all possible solutions?

Explanation:

Step1: Define inequalities

Let $x$ = number of cats, $y$ = number of dogs.

1. Total animals: $x + y \leq 20$ (rewrite as $y \leq -x + 20$)
2. Max cats: $x \leq 8$
3. Non-negative counts: $x \geq 0$, $y \geq 0$

Step2: Identify graph conditions

• $y \leq -x + 20$: Region below the line from $(0,20)$ to $(20,0)$
• $x \leq 8$: Region left of the vertical line $x=8$
• The solution is the overlap of these regions, with $x,y \geq 0$.

Step3: Match to options

Only Option C shows the overlap of the region below $y=-x+20$, left of $x=8$, and in the first quadrant.

Answer:

C. The graph with the yellow triangular region bounded by x=8, y=0, and x+y=20