https://file.aiquickdraw.com/mathbot/file/1725931155477wxq3em1b.jpg

Let's break down and solve the problem based on the image you provided.

The problem states:

- The average yearly salary of someone with a master's degree is **$36,000 less** than twice that of someone with a bachelor's degree.
- Together, two people with these educational attainments earn **$114,000**.
- We are tasked with finding the average salary for each individual degree holder.

Let:
- $ x $ be the average salary of someone with a bachelor's degree.
- $ y $ be the average salary of someone with a master's degree.

### Step 1: Set up the equations
From the problem, we have the following two conditions:

1. The master's salary is $36,000 less than twice the bachelor's salary:
   \[
   y = 2x - 36
   \]
2. The combined salary of both individuals is $114,000:
   \[
   x + y = 114
   \]

### Step 2: Solve the system of equations

We can substitute the expression for $ y $ from the first equation into the second equation:

\[
x + (2x - 36) = 114
\]

Simplify this:

\[
3x - 36 = 114
\]

Add 36 to both sides:

\[
3x = 150
\]

Divide by 3:

\[
x = 50
\]

So, the average salary of someone with a bachelor's degree is **$50,000**.

### Step 3: Find the master's degree salary

Now, use the first equation to find the master's salary:

\[
y = 2(50) - 36 = 100 - 36 = 64
\]

So, the average salary of someone with a master's degree is **$64,000**.

### Final Answer:
- The bachelor's degree holder's salary is **$50,000**.
- The master's degree holder's salary is **$64,000**.

Let me know if you need more details or have any questions!

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**Related questions:**
1. How do we solve a system of linear equations using substitution?
2. How do changes in salary affect the total earnings when one variable increases or decreases?
3. What is the importance of correctly setting up variables in word problems?
4. What other methods can be used to solve systems of linear equations?
5. Can this problem be solved using matrices or graphing?

**Tip:** Always define your variables clearly when solving word problems to avoid confusion in the setup.

Suppose the average yearly salary of an individual whose final degree is a master's is $36 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $114 thousand. Find the average yearly salary of an individual with each of these final degrees.

Learn how to solve a system of equations to find the average yearly salary of individuals with bachelor's and master's degrees. The problem involves algebraic concepts like substitution and setting up linear equations based on the given conditions.

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