Corrupt mayor shares 1/3 of his bribes with local judge. The judge also reseives bribes from litigators?

Question

and has to share 1/4 of those bribes with the mayor.

FBI determined that monetary transactions between the mayor and the judge are conducted by court clerk who passes enevolopes stuffed with cash, who also blackmailed both officials into paying him too. The mayor has to pay 1/6 of money received in each envelope from the judge, and the judge has to pay 1/8.

FBI also managed to obtain search warrant and dug up a chest packed with $500,000 cash in clerk's garden.

What combined amount of money was payed in bribes in the town?

Answer 1

J=$ judge's bribed with
and M=$ mayor's bribed with
and C=$ clerk gets to blackmail

clerk = by the envelopes
1/6 of judge to mayor
and 1/8 of mayor to judge

judge keeps 3J/4
mayor keeps 2M/3

C = 1/6*1/4*J + 1/8*1/3*M
= J/24 + M/24
= (J+M)/24
= 0.5 m

J+M = 24*0.5m
= 12 million dolars

Answer 2

This was a fun problem, because it has an answer. The clerk got (1/6)(1/4) of what the major received in bribes, and (1/8)(1/3) of what the judge received in bribes, or (1/24) of combined bribes. If 500,000 was found, the total of bribes received by the mayor and the judge is 12,000,000.