Stock Issuance Formula (Mathematicians please read!)

[why]

I've been sitting here for a while trying to find the formula for stock issuance in which a set percentage of unissued stock can be sold when only a percentage of the total stock has already been issued.

Basically, what I mean is if there's 10,000 total shares but there's two current stockholders who jointly own the company 50/50 but each partner only has 500 shares issued to his name. So 1000 shares are issued out of 10,000 available. A third party wants to buy 20% of the company -- how many shares is he to be issued?

I've been sitting here doing systems of equations and it's driving me nuts...I haven't done this much math since high school.

 

[BDC2823]

250 shares? 1,000 existing shares / .8 = 1,250 1,250 x .2 = 250 shares.

 

[why]

Awesome, thanks. I figured the divisor for the total was 1 minus the percentage but for some reason I kept overlooking it. I realize it works, but to satiate my curiosity why is the total amount of stock equal to 1 minus the percentage? I guess what I mean to ask is, what does the 1 signify? 100%?

 

[BDC2823]

Yes, 100%.