How do you solve a liter of cream has 9.2 percent butterfat how much skim milk containing 2 percent butterfat should be added to the cream to obtain a mixture with 6.4 percent butterfat?

To solve this problem, you can use the concept of weighted averages. Let ( x ) be the volume of skim milk added. The equation based on the butterfat content would be:

[ \frac{(1 , \text{L} \times 9.2) + (x \times 2)}{1 + x} = 6.4. ]

By simplifying this equation, you can solve for ( x ). Rearranging gives ( 9.2 + 2x = 6.4 + 6.4x ), leading to ( 2.8 = 4.4x ), and ultimately ( x \approx 0.636 , \text{L} ) of skim milk needed to achieve the desired butterfat percentage.