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To solve this problem, we need to represent the savings of both Charlie and Taylor with an equation and determine when they will have saved the same amount of money.

### Step 1: Formulate the Equation
- **Charlie** starts with $200 and saves $50 each week. His total savings after $ x $ weeks can be represented by:
  \[
  \text{Charlie's savings} = 200 + 50x
  \]
  
- **Taylor** starts with $0 but saves $70 each week. Her total savings after $ x $ weeks can be represented by:
  \[
  \text{Taylor's savings} = 70x
  \]

### Step 2: Set the Savings Equal
To find out after how many weeks they will have the same amount of money, we need to set their savings equal to each other:
\[
200 + 50x = 70x
\]

### Step 3: Solve for $ x $
Now, solve for $ x $:
\[
200 = 70x - 50x
\]
\[
200 = 20x
\]
\[
x = \frac{200}{20} = 10
\]

### Step 4: Fill in the Correct Answers
- The equation that represents the situation is:
  \[
  200 + 50x = 70x
  \]
  
- Charlie and Taylor will have the same amount of money after $ 10 $ weeks of saving.

### Correct Answers
1. **Equation**: $ 200 + 50x = 70x $
2. **Weeks**: 10 weeks

Would you like any more details or have any questions?

### Related Questions:
1. How would the equation change if Charlie saved $60 per week instead?
2. What if Taylor started with $100 and saved $70 weekly, how would this affect the solution?
3. How much money would Charlie and Taylor have saved after 5 weeks?
4. How would the solution change if both saved at the same weekly rate but started with different initial amounts?
5. Can you form a similar equation if the saving rate changes every few weeks?

### Tip:
Always isolate the variable step by step when solving linear equations!

Charlie and Taylor are saving for a vacation trip. Charlie already has $200 saved and plans to save an additional $50 every week. Taylor starts with nothing but plans to save $70 each week. After how many weeks will Charlie and Taylor have saved the same amount of money for their vacation?

Learn how to solve a real-world algebra problem involving Charlie and Taylor's vacation savings. This problem covers linear equations and teaches how to find out after how many weeks they will have saved the same amount of money. Suitable for students in Grades 6-8.

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