Hi Katie,
There is a typo in our equation, it should be
x  .0765x  .008x  .20x  .05x = 20,000
The problem is that you want this employees net salary to be $20,000 and there are four deductions that come off her gross salary. The deductions are 7.65%, 0.8%, 20% and 5%. If you knew her gross salary and then subtracted from it the four deductions you would end up with $20,000. That is what the equation above is saying. If you call her gross salary $x then subtracting the deductions is subtracting 0.0765x, 0.008x, 0.20x and 0.05x. Thus, in total you have deducted
7.65% + 0.8% + 20% + 5 % = 33.45% of her gross salary.
You can make the same calculation using the left side of the equation (which uses proportions rather than percentages)
x  0.0765x  0.008x  0.20x  0.05x
= x  (0.0765x + 0.008x + 0.20x + 0.05x)
= x  ( 0.0765 + 0.008 + 0.20 + 0.05)x
= x  0.3345x
Her deductions are 33.45% of her gross salary so her net salary is 100%  33.45% = 66.55% of her gross salary. Using the left side of the equation again this is
x  0.3345x = (1  0.3345)x = 0.6655x
Hence the equation simplifies to
0.6655x = 20,000
The last algebraic step is to divide both sides of the equation by 0.6655. Since ^{0.6655}/_{0.6655} = 1 the equation becomes
x = ^{20,000}/_{0.6655} = 30,052.59
I hope this helps,
Penny
