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

Answer:

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

Step-by-step 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.