IO 



In the above problems the amount of the mixture desired is 

 definite. 



In working problems in standardization it is wisest to prove the 

 answer as this will show if the results are correct. While proving 

 a problem will point out errors it will not show where mistakes have 

 been made. The proof of the above problem is as follows: 



Proof: 



It is desired to make 500 pounds of an 18% mixture which would 

 necessarily contain 90 pounds of fat (500 X .18 = 90). According to 

 our computations the 500 pounds of 18% cream will consist of 125 

 pounds of 3 % milk and 375 pound s of 2 3 % cream . If these material s 

 furnish 90 pounds of fat, the problem is worked correctly. One 

 hundred twenty-five pounds of 3% milk will contain 3.75 pounds of 

 fat: (1.25 X .03 = 3.75). Three hundred seventy-five pounds of 

 23% cream will contain 86.25 pounds of fat (375 X .23 = 86.25), 

 86.25 + 3-75 = 90 pounds of fat. 



In the following problem the amount of mixture to be made up 

 is indefinite. 



Problem 2: 



How much 23% cream must be mixed with 500 pounds of 3% milk 

 to make a mixture testing 1 8% ? Using our diagram according to the 

 directions previously given we have the following results: 



3' 



18 



15- 



5-. 



These results mean that we must mix the materials in the proportion 

 of 15 pounds of 23% cream to five pounds of 3% milk to make an 

 1 8% mixture. According to the conditions of the problem we must 

 use 500 pounds of 3% milk which is 100 times as large as the amount 

 given in the above proportion (500 -=- 5 = 100). The 23% cream and 

 the 3% milk must be kept in the proportion of 15:5 and if the 3% 

 milk is increased one hundred times the 23% cream must be increased 

 the same number of times. This would give 1500 pounds of 23% 

 cream (15 X 100 = 1500), which should be added to the 500 pounds 

 of 3% milk, giving 2000 pounds of an 18% mixture. The problem 

 may also be worked by simple proportion. 



