## ChristaB 2 years ago Another word problem - A dairy farmer wants to mix some buttermilk that is 12% butterfat with some that is 8% butterfat. If he wants to produce 100 gallons of buttermilk that is 9% butterfat, how much of each should he mix?

1. Hero

Total gallons of buttermilk: x + y = 100 Total percentage of butterfat: .12x + .08y = .09(100) Solve the system

2. ChristaB

is it 12x + 8 (100 - x) = 100 (9) --- 12x - 800x = 900 --- 788x=900 --- x=1.14

3. ChristaB

no.. that cant be it... the question asks for 'how much each should be"

4. Hero

x + y = 100 .12x + .08y = .09(100) x + y = 100 .12x + .08y = 9 .08x + .08y = 8 .12x + .08y = 9 .12x + .08y = 9 -.08x - .08y = -8 .04x = 1 x = 1/.04 x = 25 y = 75

5. mathstudent55

The final result is 100 gallons of 9% butterfat, so the farmer will have 9% of 100 gal = 9 gal of butterfat in the 100 gallons of 9% milk Let's call the amount of 8% milk x. Since the total amount will be 100 gal, the amount of 12% milk used will be 100 - x. How much butterfat is there in x gallons of 8% milk? 0.08x How much butterfat is there in (100 - x) gallons of 12% milk? 0.12(100 - x) The fat from 8% milk + the fat from 12% milk = the fat in the 9% milk 0.08x + 0.12(100 -x) = 9 0.08x + 12 - 0.12x = 9 -0.04x = -3 x = 75 75 gallons of 8% milk, 25 gallons of 12% milk