Can someone help me with a basic algebra problem?

Question

Here the question that I'm struggling with but I'm having trouble with problem C.

One employee of a furniture store is paid a base salary of $ 4000 a month plus an 6 % commision on all sales over $ 8000 during the month.

(A) How much must the employee sell in one month to earn a total of $ 9000 for the month?
$ 91333.33

A second employee of the furniture store is paid a base salary of $ 5000 a month plus 3 % commission on all sales during the month.

(B) How much must the employee sell in one month to earn a total of $ 9000 for the month?
$ 133333

(C) Determine the sales level at which both employees receive the same monthly income.
$ ???

Answer 1

Let S be the sales level.

For employee 1:
Salary = 4000 + 6% * (S - 8000)

For employee 2:
Salary = 5000 + 3% * S

(note that these formulas only work if sales exceed $8,000; but that's OK, because if sales are less than $8,000, we know employee 1 makes less than employee 2, so our answer must be above $8,000).

So:
5000 + 3% * S = 4000 + 6% * (S - 8000)
3% * S = -1000 + 6%*(S - 8000)
3% * S - 6% * (S - 8000) = -1000
3% * S - 6% * S + 6% * 8000 = -1000
-3% * S = -1000 - 6% * 8000
S = (-1000 - 6% * 8000) / (-3%) = $49,333

Answer 2

$4,000 + 6(S - $8,000)/100 = $5,000 + 3S/100
$400,000 + 6S - $48,000 = $500,000 + 3S
3S = $148,000
S = $49,333.33