Afarmer 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

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

Step-by-step 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.

i don't see any steps below, sweetheart