The bar graph which is 4% whole mil, 8% milk for cream and 30% cream shows the milk fat percentages in three dairy product s. How many pounds each of whole milk and cream should be mixed to form 200 lb of milk for cream cheese?
If using x lbs of 4% milk,
.04x + .30(200-x) = .08(200)
To determine how many pounds of whole milk and cream should be mixed to form 200 lb of milk for cream cheese, we need to use the information provided in the bar graph.
Let's start by calculating the milk fat percentages for whole milk and cream based on the given percentages:
- Whole milk: 4% milk fat
- Cream: 30% milk fat
Next, we'll assume that the whole milk and cream are the only ingredients used to make the milk for cream cheese. Since we want to make 200 lb of cream cheese, we can set up the following equation:
Total pounds of whole milk + Total pounds of cream = 200 lb
Now, let's express the milk fat percentages in terms of decimal form:
- Whole milk: 4% = 0.04
- Cream: 30% = 0.30
Based on the equation and the milk fat percentages, we can create the following two equations:
Equation 1: 0.04 * Total pounds of whole milk + 0.30 * Total pounds of cream = 0.08 * 200 lb
Equation 2: Total pounds of whole milk + Total pounds of cream = 200 lb
We have a system of two equations with two variables. To solve this system, we can use substitution or elimination methods. Let's solve it using the substitution method:
From Equation 2, we have:
Total pounds of whole milk = 200 lb - Total pounds of cream
Substitute this expression into Equation 1:
0.04 * (200 lb - Total pounds of cream) + 0.30 * Total pounds of cream = 0.08 * 200 lb
Simplify the equation:
8 lb - 0.04 * Total pounds of cream + 0.30 * Total pounds of cream = 16 lb
Combine like terms:
0.26 * Total pounds of cream = 8 lb
Solve for Total pounds of cream:
Total pounds of cream = 8 lb / 0.26
Total pounds of cream ≈ 30.77 lb
Now substitute this value back into Equation 2 to find Total pounds of whole milk:
Total pounds of whole milk = 200 lb - 30.77 lb
Total pounds of whole milk ≈ 169.23 lb
Therefore, to form 200 lb of milk for cream cheese, you would need approximately 169.23 lb of whole milk and 30.77 lb of cream.