Question

How much money would I have to earn in order to have $1000 net, if my gross income is taxed at 30% ?
What is the mathmatical formula?

Answer 1

Your net is your gross minus 30% of your gross. In numerical terms, that's: \[net=gross-\frac{30}{100}gross\]What does that equal?

Answer 2

could you show me that equation solved using $1000 as the only given variable?

Answer 3

at 30%

Answer 4

I can't give you the whole solution, but I can help you get there. Using what I wrote above, what does the net equal?

Answer 5

hold on

Answer 6

I need more help

Answer 7

Alrighty, let's pretend your gross is 100. That would make the formula: \[net=100-\frac{30}{100}\times100\] What does that equal?

Answer 8

hold on

Answer 9

net = 70

Answer 10

Exectly! What percentage of the gross does that make the net? By which I mean, what is the percentage form of \[\frac{70}{100}\]?

Answer 11

hold on

Answer 12

70% ?

Answer 13

Yep! So the net therefore is 70% of the gross. In numerical terms, \[net=70\% \times gross\]\[net=\frac{70}{100}\times gross\]
Back to the original question: If your net is $1000, what is the gross? Well, plug it into this formula: \[1000=\frac{70}{100}\times gross\]

Answer 14

hold on

Answer 15

am I solving for X and gross? or does the X mean (Times) the gross?

Answer 16

The X means times, sorry :)

Answer 17

Gross = 700

Answer 18

I'm afraid not. What steps did you take to calculate that?

Answer 19

Gross = 0.07

Answer 20

Alas, no. Could you post your work?

Answer 21

i'll try

Answer 22

how do you make the 70 over 100 look like you do?

Answer 23

It doesn't matter too much. Consider it magic for now.

If you have \[1000=\frac{70}{100}\times gross\] Your first step would be to get rid of that fraction. Firstly, get rid of the denominator. Multiply both sides of the equation by 100: \[(100)(1000)=(100)\left(\frac{70}{100}\right) \times gross\] The 100 on the top and bottom of that fraction will cancel out, leaving you with \[100000=70 \times gross\] Next, get rid of that 70. Divide both sides by 70: \[\frac{100000}{70}=\frac{70}{70}\times gross\] Again, the 70s in that fraction on the right will cancel each other out, so you are left with \[\frac{100000}{70}=gross\]

Answer 24

So the answer is 1,428.6 ?

Answer 25

Yeps.

Answer 26

You have helped me a great deal. I really appreciate it, and believe it or not I do not think it was magic. It really does make sense. Thanks again. Oh. and thanks for the medal.

Answer 27

Good luck with your future efforts!

Answer 28

Thank you