COMPOUNDING RATIONS 239 



The quantities are to be such that the protein in the cake 

 plus that in the rice will together amount to 10 Ibs. ; and the 

 " starch " in the cake plus that in the rice will together amount 

 to 60 Ibs. If the unknown quantities of cake and rice be 

 respectively designated by the symbols x and y the proposition 

 may be stated in the form of two (simultaneous) equations, 

 thus 



0*253: -j- 0*067 = 10 ; 0-56^ -f '657 = 60 



By division 



x -f- 0*247 = 40*0 ; x -f- 1*167 = 107*14 



By subtraction 



0-927 = 67-14 

 7 = 72-98 

 By substitution 



x = 40 (72*98 X 0*24) 

 x= 22*48 



A similar method may be employed to determine the 

 relative proportions instead of the actual quantities in which 

 two foods should be combined to produce a given N-ratio 

 (say 6 to i). The proposition is stated exactly as before, but 

 in this case the object is to eliminate the numerical terms, and 

 obtain x and y in terms of each other. 



2$x + 6y=i; 56* + 657 = 6 

 By division 



2$x -f 6y = i ; 9*33* + 10*837 = i 

 By subtraction 



15*67.* 4*837 = 



3*24* =7 



The proportions are 3*24 parts of rice meal to i of cake. 



Simplified Arithmetical Method. If, in the last example, 

 the symbols x and 7 be left out altogether, and we consider 

 merely the arithmetical operations involved, it will be seen 

 that they come to this, which may be regarded as the rule : 



Divide the percentages of "starch" in each food by the 



