Answer: Let's start by defining some variables:
Let x be the average yearly salary of an individual with a bachelor's degree.
Let y be the average yearly salary of an individual with a master's degree.
We are told that the average yearly salary of an individual with a master's degree is $35 thousand less than twice that of an individual with a bachelor's degree. This can be expressed mathematically as:
y = 2x - 35000
We are also told that two people with each of these educational attainments earn $115 thousand in total. Since we don't know how many people there are with each degree, let's call the number of individuals with a bachelor's degree "b" and the number of individuals with a master's degree "m". Then we can write:
bx + my = 115000
We can use this equation to solve for one of the variables in terms of the other. Let's solve for b:
b = (115000 - my) / x
Now we can substitute this expression for b into the first equation we wrote:
y = 2x - 35000
and solve for x:
(115000 - my) / x * x + my * (2x - 35000) = 115000
Simplifying this equation, we get:
115000 - my + 2mx - 35000x = 115000
Rearranging and simplifying further, we get:
(2m - 35)x = my
Substituting the expression for b that we found earlier, we get:
(2m - 35)x = (115000 - my) / x * y
Multiplying both sides by x, we get:
(2m - 35)x^2 = (115000 - my) * y
Substituting y = 2x - 35000, we get:
(2m - 35)x^2 = (115000 - my) * (2x - 35000)
Expanding and simplifying this expression, we get:
2mx^2 - 35x^2 = 230000x - myx - 115000y
Substituting y = 2x - 35000 again, we get:
2mx^2 - 35x^2 = 230000x - myx - 115000(2x - 35000)
Expanding and simplifying, we get:
2mx^2 - 35x^2 = 28000x - 115000(35000) + myx
Substituting b = (115000 - my) / x, we get:
2mx^2 - 35x^2 = 28000x - 115000(35000) + x(115000 - bx)
Simplifying further, we get:
2mx^2 - 35x^2 = 28000x - 115000(35000) + x(115000 - (115000 - my) / x)
Multiplying through by x, we get:
2mx^3 - 35x^3 = 28000x^2 - 115000(35000)x + x(115000x - (115000 - my))
Simplifying further, we get:
2mx^3 - 35x^3 = 2x^2my
Now we can substitute y = 2x - 35000 again, and simplify:
2mx^3 - 35x^3 = 2x^2(2x - 35000)
Expanding and simplifying, we get:
2mx^3 - 35x^3 = 4x^3 -
Explanation: