How to deal with unequal investment between founders and angel investor?

I have a startup company. We have an angel investor who is willing to invest $50,000 in the company for a company share of 33%. That leaves the 67% of the company share for my business partner and I. The 67% is divided among us 34% and 33% respectively. With this investment, does it mean that we, the founders have to put in 50,000/33 * (67) = $101515.152 to match the investor's contribution (50,000 for 33%) in order to own 67% of shares in the company? If yes, that would defeat the purpose of us going to an angel investor in the first place.

If no, how do we work things out? How would the shares be calculated if, the investor puts in the same 50k for 33% and we, the founders can scrape up a mere 20k for our 67% share of the company?

Examples are good, so here's a account of how we did it, which I believe is the standard way. I've changed the numbers to make it easier to understand.

When I and my two co-founders started, we each bought 10 shares in our freshly-incorporated company, paying £1 for each share. At that point we had what was effectively a shell company with just £30 in the bank, with 30 shares issued.

We then went to our investors -- we'd spoken to them before, and had agreed on prices and equity splits so on -- but at this point we all formally agreed that we all thought that the company -- with its £30 in assets, but, more importantly, the founders working for it and our business plan behind it -- was worth significantly more than its £30 assets in the bank. So they agreed to pay £10,000 for 33% of the company. This meant that we (the founders) issued another 15 shares, and sold them to the investors for the £10,000 they offered.

Once that was done, the company had 45 shares issued; the investors had 15 of them (thus, 33%) and we each had 10. Of course, that meant that we, the founders, had been diluted (my 10 shares were originally 33% of the issued ones, but now they were 10/45 = 22%) but that's what happens when you take on investment.

It also meant that the investors paid 10000/15 = just less than £666.66 per share, while I and my co-founders paid £1 per share. But these investments happened in different rounds, so that's fine. At the end of the day the price of a share is whatever buyer and sell agree on. When I bought my shares, I was just putting money into an "empty" corporate vehicle. When the investors put in their money, they were putting money into a company with a business plan, founders, and so on. So I bought into something worth very little, and they bought into something that was (we all hoped!) worth a lot more.

Hope that helps.