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130
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GANITASĀRASANGRARA.
The role for separating the prices of (an interchangeable) larger and a similar) smaller number of two different things from the given mixed sums of the prices of these things :
1391. From the higher price-sum, as multiplied by the corresponding larger number of one of the two kinds of things, subtract the lower prioe-number as multiplied by the smaller pumber relating to the other of the two kinds of things. Then divide the result by the difference between the squares of the numbers relating to these things. This gives rise to the price of the thing which is larger in number. The other, that is, the price of the thing which is smaller in number, is obtained by interchanging the multipliers.
An example in illustration thereof. 1404 to 1421. The mixed price of 9 citrons and 7 fragrant woud-apples is 107; again the mixed price of 7 citrons and 9 fragrant wood-apples is 101. O you arithmetician, tell me quickly tho price of a citron and of a wood-apple hero, having distinctly separated those prices well.
The rule for separating the prices and the numbers of different mixed quantities of different kinds of things from their given mixed price and given mixed values :
143. The (difforont) given (mixed) quantities (of the different things) are to be multiplied by an optionally chosen uumber; the given (mixed) price of these mixed quantities) is to be diminished (by the value of these products separately). The resulting quantities
139). Algebraically, if
az + by=m and bx + ay = 1, then * + aby = um and b's + aby = bn. .. (-") =an-bn.
sum - bu
143. The rule will become clear by the following working of the problem in stancas 144, and 145:-- The total pumber of fruits in the first heap is 21.
do.
second do. 29. Do.
third do. 23.
Do.
do.
