To solve this problem, we can use a mixture equation. Let's denote the following:
- \(x\) liters of 3% milk to be mixed.
- \(y\) liters of 15% cream to be mixed.
We want to find values for \(x\) and \(y\) such that when they are mixed, we get 20 liters of 6% cream.
Now, let's set up the equation based on the amounts of butterfat in the milk and cream:
1. The amount of butterfat in the 3% milk is 0.03x (since it's 3% or 0.03 as a decimal).
2. The amount of butterfat in the 15% cream is 0.15y (since it's 15% or 0.15 as a decimal).
In the final mixture (20 liters of 6% cream), the amount of butterfat will be 0.06 * 20 = 1.2 liters (since it's 6% or 0.06 as a decimal).
Now, we can set up the equation based on the total amount of butterfat:
0.03x + 0.15y = 1.2
We also have a constraint based on the total volume of the mixture:
x + y = 20
Now, you have a system of two equations with two variables:
1. 0.03x + 0.15y = 1.2
2. x + y = 20
You can solve this system of equations to find the values of \(x\) and \(y\), which will tell you how much 3% milk and 15% cream to mix.