Question

# A dairy needs 385 gallons of milk containing 5 % butterfat. How many gallons each of milk containing 8% butterfat and milk containing 1% butterfat must be used to obtain the desired 385 gallons? gallons of milk containing 8 % butterfat gallons of milk containing 1% butterfat

Answer

220 gallons of milk containing 8% butterfat and 165 gallons of milk containing 1% butterfat.

- Let x be the number of gallons of milk containing 8% butterfat, and y be the number of gallons of milk containing 1% butterfat.
- We can set up the following system of equations: x + y = 385 0.08x + 0.01y = 0.05(385)
- Simplifying the second equation, we get: 8x + y = 1925
- Subtracting the first equation from the simplified second equation, we get: 7x = 1540
- Solving for x, we get: x = 220
- Substituting x into the first equation to solve for y, we get: y = 165
- Therefore, 220 gallons of milk containing 8% butterfat and 165 gallons of milk containing 1% butterfat must be used to obtain 385 gallons of milk containing 5% butterfat.