word problem

Question

the average yearly salary of an individual whose final degree is a? master's is ?$44 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 ?$115 thousand. Find the average yearly salary of an individual with each of these final degrees.

Answer 1

Hi Lindsay!

 

You can solve this word problem using algebraic translation (translating important parts of the word problem into algebraic expressions).  Here is the algebraic translation:

 

"2x - 44,000" - Master's is 44,000 less than (subtraction), twice the bachelor's degree (multiply by 2), let x represent the bachelors degree salary

 

"+ x" - combined salary (add the bachelors variable to the expression representing the masters degree salary)

 

 " = 115,000" - combined, earn 115, 000

 

If you put all of these pieces together, your equation is: (2x - 44,000) + x = 115, 000.  Simplify and solve for x (remember, this represents the bachelors salary = 53,000).  Plug back in and you will get the value of the masters degree 62,000.  Check your work and you will find that 53,000 + 62,000 = 115,000 AND 62,000 is 44,000 less than 2 times 53,000.

 

Hope this helps!!  :)

Answer 2

Let X be the salary for the Master's degree and Y be the salary for the Bachelors.

Then,

X + Y = 115,000 and X= 2Y-44,000

 

plug the second equation for X into the 1st equation: (2Y-44,000) +Y = 115,000

Solve for Y: Y= 53,000

Plug this into the 1st equation for Y and solve for X: X + 53,000 = 115,000

X = 62,000