Final answer:
The average yearly salary of an individual with a Bachelor's degree is $51,000, and with a Master's degree is $64,000, based on the relationships given between their salaries.
Step-by-step explanation:
The question is asking to solve for the average yearly salaries of individuals with a Bachelor's degree and a Master's degree given a set of relationships between their salaries. Let's denote the average salary of an individual with a Bachelor's degree as B and with a Master's degree as M.
According to the problem, the salary of someone with a Master's is $38,000 less than twice the salary of someone with a Bachelor's degree, which can be expressed as: M = 2B - 38 (in thousands of dollars).
It's also given that combined, their salaries amount to $115,000. That can be expressed as: B + M = 115 (in thousands of dollars).
By substituting the expression for M from the first equation into the second, we get: B + (2B - 38) = 115.
Simplifying, we get 3B - 38 = 115. Solving for B, we add 38 to both sides: 3B = 115 + 38. So, 3B = 153. Dividing both sides by 3 gives us: B = 51.
Having found B, we can now find M by substituting B into the first equation: M = 2(51) - 38, which simplifies to M = 102 - 38, thus M = 64.
Therefore, the average yearly salary of an individual with a Bachelor's degree is $51,000, and with a Master's degree is $64,000.