to be respectively) multiplied by (the specified) multiple quantities (mentioned above) ; from the several products so obtained the (already found out) values of the moneys on hand are (to be separately subtracted). Then the (same) value of the money in the purse is obtained (separately in relation to each of the several moneys on hand).
An example in illustration thereof.
236-237. Three merchants saw (dropped) on the way a purse (containing money). One (of them) said (to the others), "If I secure this purse, I shall become twice as rich as both of you with your moneys on hand.” Then the second (of them) said, "I shall become three times as rich.” Then the other, (the third), said, "I shall become five times as rich.” What is the value of the money in the purses also the money on hand (with each of the three merchants) ?
The rule to arrive at the value of the moneys on hand as also the money in the purse (when particular specified fractions of this latter, added respectively to the moneys on hand with each of a given number of persons, make their wealth become in each case) the same multiple (of the sum of what is on hand) with all (the others )
238.[*] The sum of (all the specified) fractions (in the problem the denominator being ignored is multiplied by the (specified common) multiple number. From this product, the products obtained by multiplying (each of the above-mentioned) fractional parts (as reduced to a common denominator, which is then ignored), by the product of the number of cases of persons minus one and the specified multiple number this last product being diminished
238.^ The formula given in the rule is--
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where x,y,z are the moneys on hand,m the common multiplier, and a,b,c, the specified fractional parts given. |
These values can be easily found out from the following equations:-
- where P is the money in the purse.
