More Lateral Thinking

The Solution

Rav Padwa’s ruling, which he tells us was endorsed by the Tchebiner Rav, is that the the fee should be divided as follows:

• ⁶⁄₁₁ to the Shadchan
• ²⁄₁₁ to the one who supplied the boy’s name
• ³⁄₁₁ to the one who supplied the girl’s name

Rav Padwa’s fundamental premises are that:

• The promised percentages should be applied to the Shadchan’s net income, after his expenses, and not to his total revenue, and
• Each payout is considered an expense vis-a-vis his arrangement with the other partner

Expressed in the language of modern algebra, we have a simple system of three linear equations in three unknowns:

• S + B + G = 1
• B = ¹⁄₄(B + S)
• G = ¹⁄₃(G + S)

Where S is the Shadchan’s fraction of the fee and B and G are those of the partners who supplied the names of the boy and girl respectively. Substitution yields the result.

Charity and the Taxman

Perhaps a similar analysis holds in the case of one who owes fixed fractions of his income to charity and the government. Say, for example, that he has an obligation of Ma’aser to charity, and he is in a 15% tax bracket. Since the goverment allows charitable deductions when calculating income, and Ma’aser is taken from one’s net income after taxes, we can apply the above procedure, yielding:

• ¹⁷⁄₁₉₇ of his income for Ma’aser
• ²⁷⁄₁₉₇ of his income for taxes
• ¹⁵³⁄₁₉₇ for himself

Of course, this is just a plausible and reasonable solution; the correct answer in this case obviously depends on the Halachos and Minhagim of Ma’aser and the tax law as actually written, in neither of which am I expert.