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CHAPTER VIMIXED PROBLEMS.
186
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 aro (to bo separately subtracted). Then the sume) value of the money in the purse is obtained separately in relation to onch of the several moneys on hand).
* An example in illustration thereof. 236-237. Three merchants suw (dropped) on the way a purso (uontaining money). Ono (of theni) said (to the others), "If I secure this purse, I shall become twice as rich as both of you with your monoys on hand." Then the second (of them) said, "I shall become throo times as rich." Then the 'othor, (the third), said, "I shall become five timos as rich." What is the valuo of tho monoy in the purse, as also tho money on hand (with cach of the three merchants)?
Tho rule to arrive at the value of the moneys on hand am also the money in the pursu (when particular spocified fractions of this latter, added respectively to the moneys on hand with each of a given number of persons, make their wealth becomo in each case) the saniy multiple of the sum of what is on hand) with all (the others) :
238. The sum of (all the specifiod) fractions in the problom) ---the denominator being ignored--is multiplied by tho (speci. tied common) multiple number. From this product, the products obtained by multiplying each of the ubove-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 diminishod
288. The formula given in the rule is
=m (a + b + c)-a (2m-1), where x, y, are the money on hand, m
yom (+ b + c)- (2 -1), the common multiple, and a, b, c, the and =m(a + b + c)-c (2m-1), specified fractional purts given. These values can be easily found out from the following equations :
Pa +2=m (y + 2), 1
Pb + y =m (8 + x), whero P is the money in the purse. and Pc+s="(* + y))
