Adairy 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?

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

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

The correct option is E.

Step-by-step explanation:

It is given that pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours.

One hour work of A and B = 5/6

Pumps A and C, operating simultaneously, can fill the tank in 3/2 hours.

One hour work of A and C = 2/3

Pumps B and C, operating simultaneously, can fill the tank in 2 hours.

One hour work of B and C = 1/2

We need to find the how many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.

Add one hour work

A and B + A and C + B and C =

Divide both sides by 2.

Reciprocal of 1 is 1. It means ABC can fill the tank in 1 hour simultaneously. Therefore the correct option is E.