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ChristaB
 3 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?
ChristaB
 3 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?

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Hero
 3 years ago
Best ResponseYou've already chosen the best response.1Total gallons of buttermilk: x + y = 100 Total percentage of butterfat: .12x + .08y = .09(100) Solve the system

ChristaB
 3 years ago
Best ResponseYou've already chosen the best response.0is it 12x + 8 (100  x) = 100 (9)  12x  800x = 900  788x=900  x=1.14

ChristaB
 3 years ago
Best ResponseYou've already chosen the best response.0no.. that cant be it... the question asks for 'how much each should be"

Hero
 3 years ago
Best ResponseYou've already chosen the best response.1x + 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

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.1The 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
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