https://file.aiquickdraw.com/mathbot/file/1729720850190piplcxjx.jpg

Let's break down the problem step by step:

### Problem:
- Marshall starts with a salary of $36,000 and gets a $4,000 raise every year.
- Jim starts with a salary of $51,000 and gets a $1,500 raise every year.
- We need to find out how many years it will take for Marshall and Jim to have the same salary.

### Step 1: Write the salary equations for both Marshall and Jim

Let $ x $ represent the number of years it takes for their salaries to be equal.

For Marshall:
\[
\text{Marshall's salary after } x \text{ years} = 36,000 + 4,000x
\]

For Jim:
\[
\text{Jim's salary after } x \text{ years} = 51,000 + 1,500x
\]

### Step 2: Set the two salary equations equal to each other
To find out when they will have the same salary, we set their salary expressions equal to each other:
\[
36,000 + 4,000x = 51,000 + 1,500x
\]

### Step 3: Solve for $ x $
First, simplify the equation by moving all terms involving $ x $ to one side:
\[
4,000x - 1,500x = 51,000 - 36,000
\]
\[
2,500x = 15,000
\]

Now, solve for $ x $:
\[
x = \frac{15,000}{2,500} = 6
\]

### Solution:
It will take 6 years for Marshall and Jim to have the same salary.

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Let me know if you'd like any further details or have any questions! 

### Additional Questions:
1. How would the equation change if Marshall received a $5,000 raise instead of $4,000?
2. What if Jim's initial salary was $48,000 instead of $51,000?
3. How would the problem be different if Marshall and Jim both received the same raise per year?
4. What is the total salary for each after 6 years?
5. What happens if the raises stop after 6 years? Will the salaries stay the same?

### Tip:
When solving problems with two variables, setting up the correct equation by identifying what remains equal or changes over time is crucial for getting the right solution.

Marshall earns a salary of $36,000, and each year he receives a $4,000 raise. Jim earns a salary of $51,000, and each year he receives a $1,500 raise. How many years will it take before Marshall and Jim earn the same salary?

Find out how many years it will take for Marshall and Jim to have the same salary with detailed step-by-step linear equations. Marshall starts with $36,000 and a $4,000 raise each year, while Jim starts with $51,000 and a $1,500 raise annually. Suitable for students in Grades 7-9.

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