I would like to get some advice on how my business partner and I should divide the equity in our start up?

The best way to go--by far-- is to use a Grunt Fund. A Grunt Fund is a dynamic equity split model designed to provide a perfectly fair equity split for founders of bootstrapped companies. It will tell you exactly how much you and your partner and later partners and employees deserve. It's based on the relative contributions you have each made and changes over time as new contributions are made to make sure that at any given time you and your partners always have what they deserve to have- no more and no less.

The basic model is this: All contributions of time, money, ideas, relationships, supplies, equipment or anything else, can be converted into a fictional unit I call "slices". A slice is calculated based on the fair market value of the contribution and a risk multiplier.

To determine shares you simply apply this calculation:

Individual share = individual slices ÷ total slices

There is also a recovery framework that outlines what happens to shares when someone leaves the company.

I call this a "Fair & Square" split. Fair, in that it always tells you exactly the right split. And, square, because it accounts for all contributions.

I wrote a book on this model that provides detailed implementation instructions. There is also an online calculator tool on my web site. If you contact me through SlicingPie.com, I'll send you a copy of the book!

You're going to love it.

50/50 usually gets you in a gridlock in case there is a need to make a strategic decision. Allowing a 3rd member to have a small 5 to 10% could help break any indecision.

It is only natural that you feel compelled to equally divide your shares as you are starting there is "enough" romance to have a rosy outlook of everything to come. I did this with my current partner and we have been working at ease for the past 15 years.

Happy to give you more advice

This is an equation that math cannot solve. I would tell you to go back to the that moment when you told your partner you wanted him on your team. You went to him just because he could finance the first stage of the start-up? What did you and what did he/she agree on when you signed up for this project? Are you thinking about changing what has been discussed and agreed before? Sorry to add more questions than answers to your question but this things are important to understand where you stand right now.
Let's say you are right now on a 50-50 basis and you think that is unfair...to you as it sounds (but I'm not entirely sure) from your question. If you want to change that you must value all your capacities and contributions (in the past and potentially in the future) to the project in a way they can have more impact in the future than the 100 k . That is a hard exercise though. Another way to think about this is: could I get someone else to invest 100k in this project right now as it is for less than 50% of future profits? Could I get any other source of funding that would diminish the amount an investor should invest in this project? Since you are describing is a partner that only offers you money, then thinking your project without money could answer your question.
Feel free for a chat on more details over these issues and good luck!