although the position of these numbers might be reversed without 

 affecting the results. Subtract the smaller number on the left hand 

 corner of the rectangle from the number in the center and place the 

 remainder on the diagonally opposite right hand corner. Then sub- 

 tract the number in the center of the rectangle from the larger number 

 on the left hand corner and place the remainder on the diagonally 

 opposite right hand corner. The two numbers on the right hand 

 corners of the rectangle represent the number of pounds of materials 

 required. The sum of these two numbers will be a mixture containing 

 the desired percentage of fat, expressed by the number in the center 

 of the rectangle. 



In each case the number on the right hand corner of the rectangle 

 corresponds to the number on the left hand corner directly opposite. 



A few concrete examples will illustrate the rectangle method of 

 working problems in standardization. 



Problem I. How many pounds of 23 % cream and 3 % milk will be 

 required to make 500 pounds of an 18% cream? Using our diagram 

 as described above we have the following results: 



18 



15-' 



These results mean that if five pounds of 3% milk were mixed with 

 15 pounds of 23% cream the result will be 20 pounds of a mixture 

 testing 1 8%. The amount of the mixture desired was 500 pounds, 

 which is twenty-five times the amount obtained with the rectangle 

 method (500 -r- 20 = 25). If we multiply the numbers on the upper 

 and lower right hand corners of the rectangle by twenty-five we will 

 obtain respectively the pounds of 23% cream and 3% milk required 

 to make 500 pounds of an 18% mixture. These are 375 pounds of 

 23% cream (15 x 25 = 375), and 125 pounds of 3% milk (5 x 25 = 

 125). 



The problem may also be worked by simple proportion: 

 5:20 :: X : 500 



2OX = 25OO 



X = 1 2 5 pounds of 3 % milk. 

 15:20 :: X : 500 



2oX = 7500 

 X = 375 pounds of 23% cream. 



