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

What does the variable represent?

m =

Write an equation that models the situation above.
Equation:


Solve the equation.


m=         miles

In this problem, the variable $ m $ represents the number of miles that a dog is walked.

### Equation:
Let’s write an equation for the costs of both services.

- Tonya's cost: Tonya charges a flat rate of $20 per month plus $3 per mile. So her cost is:
  \[
  \text{Tonya's cost} = 20 + 3m
  \]

- Beth's cost: Beth charges $5 per mile with no monthly fee. So her cost is:
  \[
  \text{Beth's cost} = 5m
  \]

To find when the costs are the same for both services, we set the two equations equal to each other:
\[
20 + 3m = 5m
\]

### Solve the equation:
Now, let’s solve for $ m $ (the number of miles).

1. Subtract $ 3m $ from both sides:
   \[
   20 = 2m
   \]

2. Divide both sides by 2:
   \[
   m = 10
   \]

### Conclusion:
The number of miles, $ m $, for which both services cost the same is **10 miles**.

Would you like further details or explanations on any step?

Here are five related questions to consider:
1. How much does each service charge for 10 miles?
2. At what mileage is Beth's service more expensive than Tonya's?
3. How would the equation change if Tonya raised her flat rate to $25 per month?
4. What if Beth charged $6 per mile instead of $5?
5. How would the solution change if Tonya's cost per mile was reduced to $2?

**Tip:** When comparing two different rates, it helps to set up equations and solve for the point at which both rates are equal.

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. What does the variable represent? Write an equation that models the situation above. Solve the equation.

Discover how to compare two dog walking services using linear equations. Tonya charges a flat rate of $20 per month plus $3 per mile, while Beth charges $5 per mile. Learn how to write and solve the equation to find the break-even point, ideal for students in Grades 6-8.

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