A farmer has two types of milk, one that is 24% butterfat and another which is 18% butterfat. How much of each should he use to end up with 42 gallons of 20% butterfat

He should use an average of 20%, and I'm assuming, since not enough info is given, that 1 gallon of milk has the given stats. The average of 20% would mean that he needs to have a 2/3 ratio of 18 to 24, because 18:24 = 6:8, which equals 2:3, so, therefore, he needs to have 42/5 = 8.4, then 8.4*2, 9.4*3 = 16.8 and 28.2, respectively, and if you add those, you get 42. 

Hope this helps and have a nice day:)