Question

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?

Answer 1

Total gallons of buttermilk:
x + y = 100

Total percentage of butterfat:
.12x + .08y = .09(100)

Solve the system

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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