The accompanying bar graph shows the milk fat percentages in three dairy products. How many pounds each of whole milk and cream should be mixed to form

400400

lb of milk for cream​ cheese?

To solve the problem of mixing whole milk and cream to create a specific amount of milk for cream cheese, we need to:

1. Identify the milk fat percentages of whole milk, cream, and the desired cream cheese mixture.
2. Use a system of equations based on the total mass and fat content.

Let:
- \( x \) be the number of pounds of whole milk.
- \( y \) be the number of pounds of cream.
- The total mass is given as \( x + y = 400400 \) lb.

### Step 1: Understanding the percentages
Assuming typical values:
- Whole milk fat percentage is approximately 3.25%.
- Cream fat percentage is about 36%.
- Cream cheese milk fat percentage might be around 10%.

These values may vary based on your bar graph, but I'll proceed with these estimates.

### Step 2: Set up equations based on fat content
We want the total fat content in the mixture to match the fat content of cream cheese. The equation for the fat content becomes:

\[
0.0325x + 0.36y = 0.10(400400)
\]

### Step 3: Solve the system of equations
You now have two equations:
1. \( x + y = 400400 \)
2. \( 0.0325x + 0.36y = 0.10(400400) \)

I’ll solve these equations next.To form 400,400 pounds of milk for cream cheese with the desired fat percentage:

- You should mix approximately **317,875 pounds of whole milk**.
- You should mix approximately **82,525 pounds of cream**.

Would you like further details on this process or have any questions?

Here are some related questions to deepen understanding:
1. What happens if the cream cheese fat percentage changes?
2. How would the result change with different fat percentages for milk or cream?
3. Can we achieve the same goal with skim milk instead of whole milk?
4. What role does milk fat play in the texture of cream cheese?
5. How would you calculate the amount for smaller quantities of cream cheese?

**Tip:** Always check the fat percentages of ingredients before creating dairy mixtures!

The accompanying bar graph shows the milk fat percentages in three dairy products. How many pounds each of whole milk and cream should be mixed to form 400,400 lb of milk for cream cheese?

This problem explores how to mix 400,400 pounds of whole milk and cream to form milk for cream cheese with a 10% fat percentage. Using algebraic concepts and a system of linear equations, we calculate the amounts of milk and cream needed. Perfect for students in Grades 9-12 learning percentages and equation solving.

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