https://file.aiquickdraw.com/mathbot/file/1726678333867jwe3be8k.jpg

Let's define variables and set up an equation to solve the problem.

- **Peppy Pets** charges a flat fee of \$15 plus \$3 per hour.
- **Happy Hounds** charges a flat fee of \$21 plus \$1 per hour.

Let $ h $ represent the number of hours for which the total charges are the same.

### Total cost for Peppy Pets:
\[
\text{Cost}_{\text{Peppy}} = 15 + 3h
\]

### Total cost for Happy Hounds:
\[
\text{Cost}_{\text{Happy}} = 21 + 1h
\]

### Set the two costs equal to find the number of hours $ h $ when the charges are the same:
\[
15 + 3h = 21 + 1h
\]

Now, solving for $ h $:

\[
15 + 3h = 21 + 1h
\]
Subtract $ 1h $ from both sides:
\[
15 + 2h = 21
\]
Subtract 15 from both sides:
\[
2h = 6
\]
Divide by 2:
\[
h = 3
\]

Thus, the total fee charged by both companies is the same after **3 hours**.

Would you like more details or have any further questions?

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Here are 5 follow-up questions based on this problem:
1. How would the solution change if the flat fee for Peppy Pets was higher?
2. What if Happy Hounds charged \$2 per hour instead of \$1?
3. How many hours would Peppy Pets need to charge more than Happy Hounds?
4. How would you set up the equation if Peppy Pets charged \$4 per hour and Happy Hounds charged \$1.5 per hour?
5. If the flat fees were eliminated, at what hour would the two companies charge the same?

### Tip:
When comparing two linear pricing models, the key is setting the equations equal and solving for the variable representing the number of hours or units.

Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is the total fee charged by the companies the same?

Learn how to solve the linear equation problem comparing fees between Peppy Pets and Happy Hounds. Discover the solution where both companies charge the same amount based on hours. This problem covers key algebra concepts and is suitable for students in Grades 6-8.

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