COMPOUNDING RATIONS 



243 



that an indefinite number of combinations can be arranged to 

 give the specified N-ratio. 



If the quantity of any one of the three foods be fixed, 

 arbitrarily or otherwise, those of the other two are thereby 

 determined and can be calculated as before. The fixing of 

 the quantity of one of the foods gives a third equation. 

 Example : to find what quantities of cake and meal must be 

 combined with 50 Ibs. of straw to give a dietary of 10 Ibs. of 

 protein and 60 Ibs. of " starch." Let the other data be as 

 before (p. 242). The proposition may be stated thus 



o'2$x -f- o'o6y -f- o'oiz = 10 ; o'$6x -f- o'6$}> -f- o'^z 



60; z= 50 

 o'2$x -f- o'o6y = 10 (o'oi X 50) ; o'$6x -|- o'6$y 



= 60 (0-4 X 5) 



0*25.2; -j- o'o6y= 9'5 ; o'$6x -f- 0*65^ = 40 

 # = 29-28; ^ = 36-33; Z = $Q 



If 50 Ibs. of straw is used, it must be combined with 

 29'8 Ibs. of cake and 34'i6 Ibs. of meal to give 10 Ibs. of 

 protein and 60 Ibs. of starch. 



Again, suppose that 24 Ibs. of cake had been specified 

 instead of 50 Ibs. of straw, the calculation would have been 

 as follows : 



o'2$x -\- o'o6y -f- o'oiz = 10 ; o'$6x -j- o'6$y -f- o'4z = 60 



x= 24 



o'o6y -|- o'oiz = 4 o'65j> -f- o'4z = 46*56 



y = 64-83; 2=11-07; x=24 



Of the indefinite number of possible combinations of these 

 three foods which can be arranged to give the specified dietary, 

 four have been calculated above, and the results are given, for 

 comparison, in tabular form below. 



