Practical Dairy Problems 1533 



This problem may also be worked by simple proportion: 

 I 125 :: X : 500 

 25% = I X 500 

 25^ = 500 

 jc = 20, number of pounds of 28% cream there will be in the 500-lb. 

 mixture. Answer. 



If there are 20 lbs. of 28% cream in the 500-lb. mixture, the remainder 

 will necessarily be 3% milk. 



Therefore, 500 — 20 = 480, number of pounds of 3% milk. Answer. 

 The number of pounds of 3% milk can be found directly by simple 

 proportion : 



24 : 25 :: re : 500 



25^1; = 24 X 500 = 12,000 



X = 480, number of pounds of 3% milk. Answer. 



Proof: 



In working problems in standardization it is always wisest to 

 prove the answer, as this is the best method of checking the work for mis- 

 takes. According to the conditions of the problem there would be 500 lbs. 

 of 4% milk. This amount of milk would contain 20 lbs. of fat 

 (500 X .04 ^20). According to the results the 500 lbs. would be made 

 up of 480 lbs. of 3% milk and 20 lbs. of 28% cream. The 480 lbs. of 3% 

 milk would contain 14.4 lbs. of fat (480 X .03 = 14.4). The 20 lbs. of 

 28% cream would contain 5.6 lbs. of fat (20 X .28 = 5.6). 



14.4 -{- 5.6 = 20 



Since the 500 lbs. contain 20 lbs. of fat, and the materials of which the 

 500 lbs. is made up furnish the 20 lbs. of fat, the problem is worked cor- 

 rectly. 



Problem 10: 



How many pounds of 3 -per cent milk must be mixed with 150 pounds 

 of 28-per cent cream to make a mixture testing 4 per cent? In this problem 

 the number of pounds to be made up is not definitely known. 



Working the problem by the rectangle 

 scheme, we find that i part of 28% cream is ps^ 

 required for 24 parts of 3% milk. According 

 to the terms of the problem, 150 lbs. of 28% 

 cream must be used, and this is 150 times as 

 large as in the above proportion. The 28% 

 cream and 3% milk must be kept in the pro- 

 portion of I : 24, and since the amount of 28% cream is to be increased 

 150 times, the 3% milk must also be increased 150 times. This would 

 give 150 lbs. of 28% cream (i X 150) and 3,600 lbs. of 3% milk 



