Question

Suppose the average yearly salary of an individual whose final degree is a​ master's is ​$43 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 ​$116 thousand. Find the average yearly salary of an individual with each of these final degrees?

Answer 1

To find the average yearly salary of individuals with a bachelor's and master's degree, set up and solve an equation using the given information.

Step-by-step explanation:

Let's assume the average yearly salary of an individual with a bachelor's degree is represented by x. According to the question, the average yearly salary of an individual with a master's degree is $43 thousand less than twice that of a person with a bachelor's degree.

So the average yearly salary of a person with a master's degree can be represented as 2x - $43,000.

The combined earnings of two individuals, one with a bachelor's degree and another with a master's degree, is given as $116 thousand.

Therefore, we have the equation:

x + (2x - $43,000) = $116,000

By solving this equation, we can find the value of x, which represents the average yearly salary of an individual with a bachelor's degree. Then, we can substitute this value back into the expression 2x - $43,000 to find the average yearly salary of an individual with a master's degree.

Answer 2

A person who holds a master's degree would earn an average $63,000

A person who holds a bachelor's only would earn an average $53,000

Step-by-step explanation:

We will need to construct equations from the sentences.

Firstly, let the yearly average for a master's degree holder be m and that of bachelor's be b.

Now, we know that someone with a master's earn 43000 less than twice what someone with bachelors earn.

Mathematically,

m = 2b - 43,000

Combined, they have an average salary of 116,000

Mathematically,

m + b = 116,000

Now we have 2 equations to solve simultaneously.

m = 2b - 43,000 ......(i)

m + b = 116,000 .......(ii)

We can sub I into ii

2b - 43,000 + b = 116,000

2b+b = 116,000 + 43,000

3b = 159,000

b = 159,000/3 = 53,000

m = 2b - 43,000

m = 2(53,000) - 43,000 = 63,000