A dairy wishes to mix together 1,000 pints of milk that contains 8% butterfat. if the mixture is to be made from milk containing 5% butterfat, and cream containing 20% butterfat, how many pints of each is needed?

x = pints of 5% butterfat

y = pints of 20% butterfat

x + y = 1000

5x + 20y = 8*1000

put the system of linear equations into standard form

x + y = 1000

5x + 20y = 8000

Solving:

1000*0.08 = (1000-c) * 0.05 + c*0.2

80 = 50 - 0.05c + 0.2c

80-50 = (0.2-0.05) * c

30 = 0.15*c

c = 30/0.15

c = 200

m = 1000-200 = 800

Therefore,

x = pints of 5% butterfat = 800

y = pints of 20% butterfat = 200

We can write the question as a mathematical formula as follows:

1000 * 0.08 = m * 0.05 + c * 0.2

1000 = m + c

where m are pints of milk and c are pints of cream

So solving the first equation with m = 1000 - c

1000*0.08 = (1000-c) * 0.05 + c*0.2

80 = 50 - 0.05c + 0.2c

80-50 = (0.2-0.05) * c

30 = 0.15*c

c = 30/0.15

c = 200

m = 1000-200 = 800

So the dairy needs 800 pints of milk and 200 pints of cream