Interesting and unique question.
I'm going to put myself in the investor's shoes and try to answer this question.
As an investor, if the key value in this deal was the business itself, I would invest in it without your involvement. So I'm assuming both you and the investor agree that the business has value and can be grown far beyond what the current founder has done (or is able to).
So the biggest thing I'm investing is not the business, it's your ability to grow that business. As such, being able to negotiate controlling equity should be possible.
The key thing to note -- it's an early stage startup. Valuations for businesses this size are based slightly more on the future potential than a multiple of the EBITDA.
Depending on your previous track record and confidence the investor has on your abilities to grow this business, 49/51 would indeed be fair and doable.
PS. I'm sure you are, but just in case -- you are going to be on a vesting schedule, correct?
If the value of the business is significantly more than the $100K you mentioned for the purposes of this discussion, then being able to take controlling equity would be harder to sell to the investor.
Also, if you're confident about being able to grow this business, put in a small amount of your own money as well. Having skin in the game is a good way to reduce perceived risk for an investor.
Depending on your risk tolerance, you should put in some of your own money as @Nishank has suggested.
Buying the company entirely with a personal loan would be quite risky. A better option is going 50/50 (in terms of money invested) with the investor. In that case, offering the investor 25% equity in exchange for half the investment would be fair.
A much simpler calculation that would make everyone happy.