Help me quick, please . . . . I'd be so grateful. It's been 30 years since I've been in an algebra class and, for my job, I really need to understand (spelled out step by step) how to gross up payroll wages. Here's the formula and answer; I need to see the steps taken to get to the answer. Thank you so much in advance:

x -.765x -.008x -.20x -.05x = 20,000

x = 30,052.59

please show me what happened to get that answer (I know I can use a gross up calculator online, but my boss expects me to understand the algebra! I'm 53 years old and haven't had algebra since college!)

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