From the year c. 850 the book Ganita-Sara-Sangraha
contains the following:
Three merchants saw in the road a purse. One said, "If I secure this purse, I shall become twice as rich as both of you together."
Then the second said, "I shall become three times as rich."
Then the third said, "I shall become five times as rich."
What is the value of the money in the purse, as also the money on hand?
There are an infinite number of solutions. Find the smallest whole number amounts the merchants could have.
(In reply to Analytical Solution (spoiler)
by Steve Herman)
I'm not posting my solution , which began:
Since all relations in the puzzle are linear we can assume WLOG that we are looking for the triplet of integers (1,x,y) such that 2x+2y=S+1
...the rest is isomorphic with your solution.
If no integer values were found, multiplying the results by complying factor would provide the correct result.
Edited on July 19, 2017, 6:53 am