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We are asked to find how many minutes of calls will make the costs of two phone plans equal.

### Step 1: Set up the equations for both plans.

Let $ x $ be the number of minutes of calls.

- **First Plan:**
  Monthly fee: $20  
  Additional cost per minute: $0.13  

  Total cost for this plan:  
  \[ C_1 = 20 + 0.13x \]

- **Second Plan:**
  Monthly fee: $10  
  Additional cost per minute: $0.17  

  Total cost for this plan:  
  \[ C_2 = 10 + 0.17x \]

### Step 2: Set the costs equal to find when the plans cost the same.
\[
20 + 0.13x = 10 + 0.17x
\]

### Step 3: Solve the equation.
Subtract 10 from both sides:
\[
10 + 0.13x = 0.17x
\]

Subtract $ 0.13x $ from both sides:
\[
10 = 0.04x
\]

Divide by 0.04:
\[
x = \frac{10}{0.04} = 250
\]

### Conclusion:
The costs of the two plans will be equal when the number of minutes of calls is **250 minutes**.

Would you like further details or have any questions? Here are five related questions:

1. What will be the cost of each plan if the number of minutes exceeds 250?
2. How much would each plan cost if the calls lasted for 100 minutes?
3. For very high usage (e.g., 500 minutes), which plan becomes cheaper?
4. What are some other factors customers might consider besides cost per minute?
5. How could this problem change if additional fees or discounts were involved?

**Tip:** When solving equations, always ensure you simplify and balance terms on both sides step by step.

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $20 monthly fee and charges an additional $0.13 for each minute of calls. The second plan has a $10 monthly fee and charges an additional $0.17 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Learn how to solve a cost comparison problem between two phone plans with different monthly fees and per-minute charges. This algebra problem involves setting up linear equations and solving for the number of minutes when the costs are equal. Ideal for students in Grades 6-8.

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