Gabe and his sister Lola both got new cell phones. Gabe bought his phone for $350, and his plan costs $30 per month. Lola bought her phone for $140, but because she added an extended warranty, her plan costs $44 per month.
After how many months will Gabe and Lola have spent the same amount on their cell phones and plans?

Let's define the variables and set up the equations to solve this problem:

- Let $ x $ represent the number of months.
- Gabe's total cost after $ x $ months will be the sum of his phone cost and his monthly plan:  
  \[
  \text{Gabe's total cost} = 350 + 30x
  \]
- Lola's total cost after $ x $ months will be the sum of her phone cost and her monthly plan:  
  \[
  \text{Lola's total cost} = 140 + 44x
  \]

We are asked to find after how many months their total costs will be equal. This gives us the equation:
\[
350 + 30x = 140 + 44x
\]

### Solving the equation:
1. Subtract $30x$ from both sides to simplify:
   \[
   350 = 140 + 14x
   \]
2. Subtract 140 from both sides:
   \[
   210 = 14x
   \]
3. Divide both sides by 14:
   \[
   x = \frac{210}{14} = 15
   \]

So, after 15 months, Gabe and Lola will have spent the same amount on their cell phones and plans.

Would you like further clarification or more details on this solution?

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Here are 5 related questions:
1. How much will Gabe and Lola each have spent after 15 months?
2. What will be their respective costs after 12 months?
3. If Gabe increases his monthly plan to $35, after how many months would their costs equal again?
4. How much more will Lola spend compared to Gabe after 18 months?
5. What is the total amount Gabe and Lola will spend combined after 20 months?

**Tip:** When solving equations with multiple variables, always aim to simplify the equation by isolating one variable at a time.

Gabe and his sister Lola both got new cell phones. Gabe bought his phone for $350, and his plan costs $30 per month. Lola bought her phone for $140, but because she added an extended warranty, her plan costs $44 per month. After how many months will Gabe and Lola have spent the same amount on their cell phones and plans?

Discover how to solve a real-world problem involving linear equations. Gabe and Lola purchased new cell phones with different costs and monthly plans. Learn how to calculate after how many months their total spending will be the same. Suitable for Grades 6-8.

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