As a dog walker, Hannah can walk at most 15 dogs per day. She charges $$ \$ 14 $$ per walk for small dogs and $$ \$ 16 $$ per walk for large dogs. Hannah needs to earn at least $$ \$ 170 $$ per day. Write two inequalities to model this situation. Let $$ x $$ be the number of small dogs Hannah walks and $$ y $$ be the number of large dogs Hannah walks. Answer 2Points

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The two inequalities that model Hannah's situation are:

1. **Total dogs constraint:**
   $$
   x + y \leq 15
   $$
   (Hannah can walk at most 15 dogs per day.)

2. **Earnings requirement:**
   $$
   14x + 16y \geq 170
   $$
   (Hannah needs to earn at least \$170 per day.)

**Final Answer:**
$$
\begin{cases}
x + y \leq 15 \
14\,x + 16\,y \geq 170
\end{cases}
$$
The two inequalities are: 1. $$ x + y \leq 15 $$ (total dogs) 2. $$ 14x + 16y \geq 170 $$ (earnings)

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