The problem is almost insanely worded, at least as you have paraphrased it. Please give the exact and complete wording of the problem. Perhaps it was not written by a chimpanzee.
Purchase price = 275.
Sales price = 325.
Is that correct?
Net gain = profit = 325 - 275 = 50.
Proceeds from the transaction are obviously 325, and profit on the transaction is just as obviously 50.
Now what do the almost incoherent words "when the property is sold, (as long as it sells for a profit) the man will pay her back from the equity. any profit above that is split 50/50." Above what? The "equity" in what: the property or the profit. How are the two apparently competing rights to be conjoined? This is why people hire lawyers: to make sure that the words clearly delineate what the mutual intention of the parties is.
In contract negotiation, there is something called a "red line," which shows where the different drafts of a contract alter. I used to read the redline very, very carefully, word by word, to make sure that it seemed to capture the intent of what I thought had been the most recent agreement. If it did, I would then reread the entire contract, phrase by phrase, clause by clause, to make sure that a judge reading it could not help but understand it as I believed it was intended to be read as a whole. Drafting contracts is a painstaking business of understanding English prose.
Here is ONE interpretation of the incoherent mess that you have provided. The intention may well have been that, if there was a profit, each partner would share 50-50 in that profit after each received back his or her FINAL NET investment. (I am not sure that was what was intended. Possibly only God knew whether these parties even reached a meeting of the minds, and no contract is valid unless there is reasonably demonstrable evidence of a meeting of the minds. God, however, is almost never deposed as a witness; service of process is exceedingly difficult.)
If that was the intended meaning, initially the capitalization was
[MATH]x + 40 + x = = 275 \implies 2x = 235 \implies x = 117.5.[/MATH]
The man contributes 117.5 + 40 = 157.5, and the woman contributes 117.5, for a total of
[MATH]157.5 + 117.5 = 275.0 \ \checkmark. [/MATH]
However, after the second transaction, the respective capitalizations are:
[MATH]157.5 - 75 = 82.5 \text { and } 117.5 + 75 = 192.5.[/MATH]
Let's check.
[MATH]82.5 + 192.5 = 275.0 \ \checkmark .[/MATH]
Now assuming we are guessing correctly what was intended by the ignorant fool of an academic who wrote this exercise,
the proceeds are divided 192.5+25=217.5 to the woman, representing half the profit plus what she eventually contributed to the joint investment, and 82.5 + 25 = 107.5 to the man.
Profits of 50 are divided equally, 25 to each.
The principal is fully distributed based on the final investments of each party:
217.5+107.5= 325.0.
That is a commercially reasonable answer in equity given the gobbldy gook you provided. Whether the academic who wrote the exercise intended that as an answer is of course unknowable. You might as well consult a Ouija board.
