Question

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?

Answer 1

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

Answer 2

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