So, I cannot find the appropriate equation to solve the following word problem:
Ernie owns 20% of a partnership that owns 76.3% of a house. The other 23.7% is owned by Sonny. Ernie wants to own exactly 49% of this house, and will have to purchase x% from the partnership and Sonny on a pro-rata basis in order to get his total interest of the home to 49%.
So, I've set up the equation as such:
49% = .2(.763) -.2x + z
.49 = .1526 -.2x + z
But I know it is not right. My confusion is that he already owns 15.26% of the house, and through the partnership he is a member of, so he really only needs to acquire 33.74% in order to get him to 49%. However, in order to keep the rest of the ownership on a pro-rata basis, (which is to say the partnership's interest and well as Sonny's will be reduced according to the ratio of their current ownership) it seems like I'm chasing my tail!!
Please let me know what you guys think. My excel worksheet is really starting to annoy me with all the circular equation warnings.