Find the average yearly salary of an individual with each of these final degrees.

Question

Suppose the average yearly salary of an individual whose final degree is a master's is $35 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 $118 thousand.

Answer 1

Let m = yearly salary of the individual with the masters degree and b = yearly salary of the individual with a bachelor degree

You can write a system of equations to describe the conditions

(a) m = 2b - 35000

(b) m + b = 118000

You can choose to solve this system of equations either by substitution or elimination. I'll show you the substitution method. The italics following each step describe the step/action I took so you can follow along.

m + b = 118000 [Equation (b)] (1)

m = 118000 - b [Subtract b from both sides] (2)

m = 2b - 35000 [Equation (a)] (3)

118000 - b = 2b - 35000 [Plug equation in line (2) for m] (4)

153000 -b = 2b [Add 35000 to both sides] (5)

3b = 153000 [Add b to both sides] (6)

b = 51000 [divide both sides by 3] (7)

m = 118000 - b [Equation in line 2] (8)

m = 118000 - 51000 [plug line 7 for b] (9)

m = 67000 (10)

Thus, we have b=51000 and m=67000

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