Tonya’s dog-walking service charges a flat rate of $20 per month, plus $3 per mile that each dog is walked. Beth does not charge a monthly fee for her dog-walking service, but she charges $5 per mile that each dog is walked.

Choose the equation that can be used to find the number of miles m for which Tonya and Beth would charge the same amount to walk one dog.
	A.	20 + 3m = 5m
	B.	20 = 3m + 5m
	C.	20 + 5m = 3m
	D.	20 + m = 8m

The solution is  
 miles.


To solve the problem, let's break down the information provided for each service:

- **Tonya's service:** Charges a flat rate of $20 per month plus $3 per mile.
  - Cost for Tonya's service: $ 20 + 3m $
  
- **Beth's service:** Charges $5 per mile, with no monthly fee.
  - Cost for Beth's service: $ 5m $

We need to find the number of miles $ m $ for which Tonya and Beth charge the same amount. This means we set the costs equal to each other:

\[
20 + 3m = 5m
\]

This corresponds to option **A**.

### Solving the equation:

1. Start with the equation:
   \[
   20 + 3m = 5m
   \]
   
2. Subtract $ 3m $ from both sides:
   \[
   20 = 2m
   \]
   
3. Divide both sides by 2:
   \[
   m = 10
   \]

So, the number of miles for which Tonya and Beth charge the same amount is **10 miles**.

If you have any questions or would like more details, feel free to ask! 

Here are 5 related questions:

1. What would be the cost for Tonya’s service if the dog is walked for 15 miles?
2. If Beth reduces her charge per mile to $4, what would the new equation be?
3. How much does Tonya charge for walking 5 miles?
4. At what number of miles would Beth's service become cheaper than Tonya’s?
5. What is the difference in cost for walking 8 miles between the two services?

**Tip:** When comparing linear costs, setting up an equation helps determine the point of balance where both costs are equal.

Discover how to compare costs between Tonya's and Beth's dog-walking services using linear equations. Solve for the number of miles at which both services charge the same amount. Suitable for grades 6-8 students learning about linear equations and cost functions.

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