https://file.aiquickdraw.com/mathbot/file/1726797698669rsefwtfv.jpg

Let's break down the problem and solve it step by step:

1. **Initial Sales & Monthly Increase**:
   - **Caleb** starts with $\$140$ and plans to increase his sales by $\$35$ per month.
   - **Nora** starts with $\$200$ and plans to increase her sales by $\$25$ per month.

2. **Goal**:
   - We need to find how many months ($x$) it will take for Caleb and Nora to have the same amount of sales.

### Step 1: Formulate the equation

Let $x$ represent the number of months after which their sales will be equal.

- **Caleb's sales after $x$ months**:  
  $140 + 35x$
- **Nora's sales after $x$ months**:  
  $200 + 25x$

Since we're looking for when their sales are equal, set the two expressions equal to each other:

\[
140 + 35x = 200 + 25x
\]

### Step 2: Solve the equation

Now, let's solve this equation for $x$:

1. Subtract $25x$ from both sides:

   \[
   140 + 10x = 200
   \]

2. Subtract $140$ from both sides:

   \[
   10x = 60
   \]

3. Divide by $10$ to isolate $x$:

   \[
   x = 6
   \]

### Answer:
- The equation representing the situation is:  
  \[
  140 + 35x = 200 + 25x
  \]

- Caleb and Nora will have the same sales after **6 months**.

---

Let me know if you'd like further clarification or details!

### Related Questions:
1. How would the equation change if Caleb increased his sales by $\$50$ per month instead of $\$35$?
2. What if Nora started with $\$250$ instead of $\$200$?
3. How many months would it take if Nora increased her sales by $\$30$ per month?
4. If both Caleb and Nora start with the same initial sales, after how many months will their sales be equal with the given monthly increases?
5. What if Caleb increased his sales by a different amount every month, say $\$35, \$40, \$45$, and so on?

### Tip:
When solving for equality in situations like this, always set up expressions for both variables and find the point where they become equal.

Caleb and Nora work at the local bookstore. Caleb has an initial sales tally of $140 for the month and he plans to increase his sales by $35 each month. Nora starts with a higher initial tally of $200, but plans to add $25 monthly. After how many months will Caleb and Nora have the same sales amount?

Learn how to solve a linear equation where Caleb and Nora's monthly sales increase at different rates. Find out how long it will take for their sales amounts to become equal using basic algebra. Perfect for students in Grades 6-8.

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