9. Milk and cream contain different percents of butterfat. How much $3 \%$ milk needs to be mixed with how much $15 \%$ cream to give 20 L of $6 \%$ cream?
Answer
Final Answer: The solution to the problem is \(\boxed{x = 15}\) and \(\boxed{y = 5}\). This means that 15 L of 3% milk needs to be mixed with 5 L of 15% cream to give 20 L of 6% cream.
Step 1 ：Let's denote the volume of the 3% milk as x (in liters) and the volume of the 15% cream as y (in liters).
Step 2 ：We can set up two equations based on the volume and the percentage of butterfat.
Step 3 ：The first equation is based on the total volume: \(x + y = 20\).
Step 4 ：The second equation is based on the total percentage of butterfat: \(0.03x + 0.15y = 0.06 * 20\).
Step 5 ：Solving these two equations gives us the values of x and y.
Step 6 ：The solution to the equations is \(x = 15\) and \(y = 5\).
Step 7 ：Final Answer: The solution to the problem is \(\boxed{x = 15}\) and \(\boxed{y = 5}\). This means that 15 L of 3% milk needs to be mixed with 5 L of 15% cream to give 20 L of 6% cream.
