Answer:
<u>800 pints</u> of 5% butterfat and <u>200 pints</u> 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.](https://tex.z-dn.net/?f=x.)
And the pints of 20% butterfat be ![y.](https://tex.z-dn.net/?f=y.)
<em>So, the total pints of milk:</em>
![x+y=1000](https://tex.z-dn.net/?f=x%2By%3D1000)
......(1)
<em>As, given:</em>
<em>1,000 pints of milk that contains 8% butterfat.</em>
<em>The mixture of milk containing 5% butterfat, and cream containing 20% butterfat.</em>
According to question:
![5(x)+20(y)=8(1000)](https://tex.z-dn.net/?f=5%28x%29%2B20%28y%29%3D8%281000%29)
![5x+20y=8000](https://tex.z-dn.net/?f=5x%2B20y%3D8000)
Substituting the value of
from equation (1):
![5(1000-y)+20y=8000](https://tex.z-dn.net/?f=5%281000-y%29%2B20y%3D8000)
![5000-5y+20y=8000](https://tex.z-dn.net/?f=5000-5y%2B20y%3D8000)
![5000+15y=8000](https://tex.z-dn.net/?f=5000%2B15y%3D8000)
<em>Subtracting both sides by 5000 we get:</em>
![15y=3000](https://tex.z-dn.net/?f=15y%3D3000)
<em>Dividing both sides by 15 we get:</em>
![y=200.](https://tex.z-dn.net/?f=y%3D200.)
<em>The pints of 20% butterfat = 200 pints.</em>
Now, to get the pints of 5% butterfat we put the value of
in equation (1):
![x=1000-y](https://tex.z-dn.net/?f=x%3D1000-y)
![x=1000-200](https://tex.z-dn.net/?f=x%3D1000-200)
![x=800.](https://tex.z-dn.net/?f=x%3D800.)
<em>The pints of 5% butterfat = 800 pints.</em>
Therefore, 800 pints of 5% butterfat and 200 pints of 20% butterfat is needed.