how much skim milk should be added to 8 gallons of 4% butterfat milk to make a milk that is 1% butterfat? 

To solve this problem, we can set up a system based on the concept of mixtures and percentages.

Let’s define the variables and information:

- You have 8 gallons of milk with 4% butterfat.
- You want to add skim milk (0% butterfat) to achieve 1% butterfat.
- Let \( x \) be the number of gallons of skim milk to be added.

### Step-by-Step Solution:
The total amount of butterfat in the 8 gallons of 4% butterfat milk is:
\[
\text{Butterfat from 8 gallons} = 8 \times 0.04 = 0.32 \text{ gallons of butterfat}.
\]

Now, after adding \( x \) gallons of skim milk, the total volume of the mixture becomes \( 8 + x \) gallons. The butterfat content should be 1% of this total volume:
\[
\text{Butterfat in the final mixture} = 0.01 \times (8 + x) \text{ gallons}.
\]

Since the butterfat content remains the same before and after adding the skim milk, we can set up the equation:
\[
0.32 = 0.01 \times (8 + x).
\]

### Solve the equation:
1. Expand the right side:
\[
0.32 = 0.01 \times 8 + 0.01 \times x.
\]
\[
0.32 = 0.08 + 0.01x.
\]

2. Subtract 0.08 from both sides:
\[
0.32 - 0.08 = 0.01x,
\]
\[
0.24 = 0.01x.
\]

3. Solve for \( x \):
\[
x = \frac{0.24}{0.01} = 24.
\]

### Final Answer:
You should add **24 gallons of skim milk** to the 8 gallons of 4% butterfat milk to create a mixture with 1% butterfat.

Would you like further details or clarifications on any part of this process?

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Here are 5 related questions:
1. How would the solution change if the original milk had 3% butterfat instead?
2. What if you wanted to make a 2% butterfat milk instead of 1%?
3. How does adding non-fat milk affect the overall volume and fat content?
4. How would this problem be solved if you were working with liters instead of gallons?
5. Can this approach be applied to other mixture problems involving percentages?

**Tip:** In mixture problems, setting up the equation based on total substance amounts (like butterfat here) helps to balance the equation easily.

how much skim milk should be added to 8 gallons of 4% butterfat milk to make a milk that is 1% butterfat?

Learn how to solve the mixture problem of adding skim milk to 8 gallons of 4% butterfat milk to achieve 1% butterfat. This solution involves understanding mixture problems, using percentage calculations, and solving algebraic equations. Ideal for students in Grades 8-10.

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