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

800 pints of 5% butterfat and 200 pints of 20% butterfat is needed.

Explanation:

Given:

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.

Now, to find the pints of each is needed.

Let the pints of 5% butterfat be
`x.`

And the pints of 20% butterfat be
`y.`

So, the total pints of milk:

`x+y=1000`

`x=1000-y` ......(1)

As, given:

1,000 pints of milk that contains 8% butterfat.

The mixture of milk containing 5% butterfat, and cream containing 20% butterfat.

According to question:

`5(x)+20(y)=8(1000)`

`5x+20y=8000`

Substituting the value of
`x` from equation (1):

`5(1000-y)+20y=8000`

`5000-5y+20y=8000`

`5000+15y=8000`

Subtracting both sides by 5000 we get:

`15y=3000`

Dividing both sides by 15 we get:

`y=200.`

The pints of 20% butterfat = 200 pints.

Now, to get the pints of 5% butterfat we put the value of
`y` in equation (1):

`x=1000-y`

`x=1000-200`

`x=800.`

The pints of 5% butterfat = 800 pints.

Therefore, 800 pints of 5% butterfat and 200 pints of 20% butterfat is needed.