Questions: As a dog walker, Hannah can walk at most 15 dogs per day. She charges 10 per walk for small dogs and 19 per walk for large dogs. Hannah needs to earn at least 190 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.

As a dog walker, Hannah can walk at most 15 dogs per day. She charges 10 per walk for small dogs and 19 per walk for large dogs. Hannah needs to earn at least 190 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.

Transcript text: As a dog walker, Hannah can walk at most 15 dogs per day. She charges $10 per walk for small dogs and $19 per walk for large dogs. Hannah needs to earn at least $190 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.

Solution

Solution Steps

Step 1: Define Variables

Let $ x $ be the number of small dogs Hannah walks and $ y $ be the number of large dogs Hannah walks.

Step 2: Formulate the Inequality for the Number of Dogs

Hannah can walk at most 15 dogs per day. Therefore, the inequality is: \[ x + y \leq 15 \]

Step 3: Formulate the Inequality for Earnings

Hannah charges $10 per walk for small dogs and $19 per walk for large dogs. She needs to earn at least $190 per day. Therefore, the inequality is: \[ 10x + 19y \geq 190 \]