Amanda's pet daycare service charges a flat rate of 25$ per month, plus 7$ per hour that each pet is taking care of. AMmara does not charge a monthly fee for her daycare service, but she charges 12$ per hour that each pet is taking care of. Write an equation that can be used to find the number of hours h for which amanda and ammara would charge the same amount. What does the variable represent?

To find the number of hours $ h $ for which Amanda and Ammara charge the same amount, we need to set up equations for the total cost each would charge based on the number of hours of pet care.

### Amanda's Total Cost:
Amanda charges a flat rate of 25 dollars per month plus 7 dollars per hour. The total cost Amanda charges can be represented as:
\[
\text{Cost}_{\text{Amanda}} = 25 + 7h
\]
Where:
- 25 is the flat monthly rate.
- $ h $ is the number of hours of care.
- 7 is the hourly rate.

### Ammara's Total Cost:
Ammara does not charge a monthly fee, but she charges 12 dollars per hour. The total cost Ammara charges can be represented as:
\[
\text{Cost}_{\text{Ammara}} = 12h
\]
Where:
- $ h $ is the number of hours of care.
- 12 is the hourly rate.

### Equation for Equal Charges:
To find when Amanda and Ammara charge the same amount, set their total costs equal to each other:
\[
25 + 7h = 12h
\]
Now, solve for $ h $.

### Solving the Equation:
1. Subtract $ 7h $ from both sides:
   \[
   25 = 5h
   \]
2. Divide both sides by 5:
   \[
   h = 5
   \]

### Interpretation:
The variable $ h $ represents the number of hours for which both Amanda and Ammara would charge the same amount. In this case, if a pet is taken care of for 5 hours, both Amanda and Ammara will charge the same total cost.

Would you like more details or have any questions?

---

**Related Questions:**
1. How much does Amanda charge if she takes care of a pet for 10 hours?
2. How much does Ammara charge for 8 hours of pet care?
3. For how many hours does Amanda charge more than Ammara?
4. What is the total cost difference if a pet is taken care of for 6 hours?
5. If Amanda increases her hourly rate to 8$, at how many hours will they charge the same?

**Tip:** When comparing costs, setting equations equal helps find the point of equality!

Amanda's pet daycare service charges a flat rate of 25$ per month, plus 7$ per hour that each pet is taking care of. Ammara does not charge a monthly fee for her daycare service, but she charges 12$ per hour that each pet is taking care of. Write an equation that can be used to find the number of hours h for which Amanda and Ammara would charge the same amount. What does the variable represent?

Find out how to solve the linear equation comparing Amanda and Ammara's pet daycare charges. Amanda charges a flat fee of $25 plus $7 per hour, while Ammara charges $12 per hour with no monthly fee. Learn how to find the number of hours where their costs are equal. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation