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Let's break down the problem:

1. **Initial Amounts:**
   - Edy starts with $450 in her savings account.
   - Juan starts with $975 in his checking account.

2. **Monthly Changes:**
   - Edy deposits $40 each month, so her monthly increase is +$40.
   - Juan writes a check for $45 each month for his cell phone bill and $20 for his water bill, so his total monthly decrease is -$45 - $20 = -$65.

3. **Equations:**
   Let's set up equations for the amounts Edy and Juan have after $ x $ months:
   - **Edy's account:** $ 450 + 40x $
   - **Juan's account:** $ 975 - 65x $

4. **Finding When the Amounts are Equal:**
   Set Edy's and Juan's amounts equal to each other:
   \[
   450 + 40x = 975 - 65x
   \]
   Solving for $ x $:
   \[
   40x + 65x = 975 - 450 \\
   105x = 525 \\
   x = \frac{525}{105} \\
   x = 5
   \]

After 5 months, Edy and Juan will have the same amount of money in their accounts.

Do you want more details on this solution or have any other questions?

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Here are 5 related questions:

1. If Edy starts with a different amount, say $600, how many months will it take for them to have equal amounts?
2. What if Juan's monthly expenses change to $50 and $30, how will the result be affected?
3. How much money will each have after 10 months?
4. Can you create a graph showing the amounts over time for both accounts?
5. What is the total amount deposited/withdrawn by each person over 5 months?

**Tip:** Always check if the changes are linear or exponential in these types of problems to set up the correct equations.

Edy has $450 in her savings account. She deposits $40 each month. Juan has $975 in his checking account. He writes a check for $45 each month for his cell phone bill. He also writes a check for $20 each month for his water bill. After how many months will Edy and Juan have the same amount of money in their accounts?

Explore how to determine the number of months needed for two accounts to have the same balance, given different initial amounts and monthly changes. This problem uses linear equations and is ideal for students in Grades 7-9.

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