Question

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

Answer 1

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:)

Answer 2

28 gallon of 24% butterfat and 14 gallon of 18% butterfat.

Explanation:

Let x gallon of 24% butterfat mixed with the y gallon of 18% butterfat to obtain 42 gallon of 20% butterfat,

⇒ x + y = 42 ⇒ x = 42 - y ----(1),

Quantity of butterfat in x gallon + quantity of butterfat in y gallon = total quantity of butterfat,

⇒ 24% of x + 18% of y = 20% of 42

⇒ 0.24x + 0.18y = 0.20 × 42

⇒ 0.24x + 0.18y = 8.4

⇒ 24x + 18y = 840

⇒ 4x + 3y = 140

From equation (1),

4(42-y) + 3y = 140

168 - 4y + 3y = 140

168 - y = 140

⇒ y = 28,

Again from equation (1),

x = 42 - y = 42 - 28 = 14,

Hence, 28 gallon of 24% butterfat and 14 gallon of 18% butterfat.