Aaron has $177 in his bank account and deposits $48 per month into his account. Claire has $79 and deposits $62 per month into her account.

Enter the number of months it will take for both Aaron and Claire to have the same amount of money in their accounts.

Let's solve the problem step by step.

1. **Aaron's Account:**
   - Initial amount: $177
   - Monthly deposit: $48
   - After $ t $ months, Aaron will have: $ 177 + 48t $

2. **Claire's Account:**
   - Initial amount: $79
   - Monthly deposit: $62
   - After $ t $ months, Claire will have: $ 79 + 62t $

We need to find the number of months $ t $ when Aaron and Claire have the same amount in their accounts, so we set their amounts equal:

\[
177 + 48t = 79 + 62t
\]

Now, solve for $ t $:

\[
177 - 79 = 62t - 48t
\]
\[
98 = 14t
\]
\[
t = \frac{98}{14} = 7
\]

So, it will take **7 months** for both Aaron and Claire to have the same amount of money in their accounts.

Would you like any details or have any questions? 

Here are 5 questions to expand your understanding:

1. What will the amount in both accounts be after 7 months?
2. How much more will Claire have after 10 months compared to Aaron?
3. If Aaron increases his monthly deposit by $10, how will that affect the number of months required for their balances to match?
4. What if Claire started with $100 instead of $79, how many months would it take then?
5. How would the scenario change if Aaron and Claire's deposit amounts were reversed?

**Tip:** Always set up an equation when dealing with unknowns; it helps in solving for the variable efficiently.

Learn how to calculate when Aaron and Claire will have the same amount of money in their bank accounts. Follow a step-by-step solution involving linear equations and arithmetic sequences. Suitable for students in Grades 6-8.

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