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!