The accompanying bar graph shows the milk fat percentages in three dairy products. A=whole milk @4%. B= milk for cream cheese @8%, and C= cream @30%. How many pounds each of whole milk and cream should be mixed to form 200 lb of milk for cream cheese?

How many pounds of whole milk will be needed?
How many pounds of cream will be needed?

507.69 FOR FIRST ONE SECOND NOT FOUND YET.

Ah, we're getting down to the dairy business now! To find out how many pounds of whole milk and cream we need to mix for our cream cheese delight, let's break it down.

Let's say we need x pounds of whole milk and y pounds of cream. Since the total weight of our creamy concoction is 200 pounds, we can set up two equations to solve this puzzling dairy problem.

First, let's consider the milk fat percentages. The fat percentage in whole milk is 4%, and in cream, it's a whopping 30%. Since we're aiming for a fat percentage of 8% for our cheese, we can create our first equation:

(4*x) + (30*y) = 8 * 200

But wait, we don't just want to know how creamy our cheese will be, we also need to make sure we have enough whole milk and cream to make it, right?

So, our second equation will focus on the total weight of our ingredients:

x + y = 200

Now we have a nice little system of equations to play with. Solve it, and you'll find the answers you seek: the pounds of whole milk needed and the pounds of cream required.

Just keep in mind that while the solution may be dairy serious, the process is all about having a little fun with numbers. Good luck getting the perfect milk-to-cream ratio for your cream cheese creation!

To determine how many pounds of whole milk and cream should be mixed to form 200 pounds of milk for cream cheese, we need to set up a system of equations.

Let's assume x pounds of whole milk and y pounds of cream are mixed.

According to the given information:

1. The milk fat percentage in whole milk (A) is 4%, which means there are 0.04x pounds of milk fat in x pounds of whole milk.
2. The milk fat percentage in cream (C) is 30%, which means there are 0.30y pounds of milk fat in y pounds of cream.
3. The milk fat percentage in the final mixture (milk for cream cheese) is 8%, which means there should be 0.08(200) = 16 pounds of milk fat in the total mixture.

Now, we can set up the equations based on the milk fat content:

Equation 1: The total pounds of whole milk fat + the total pounds of cream fat = the desired pounds of milk fat in the mixture.
0.04x + 0.30y = 16

Equation 2: The total pounds of whole milk + the total pounds of cream = the desired total weight of the mixture.
x + y = 200

We now have a system of two equations that we can solve simultaneously to find the values of x and y.

To solve the system of equations, we can use the substitution or elimination method.

Let's solve it using the substitution method:

Solve Equation 1 for x:
0.04x = 16 - 0.30y
x = (16 - 0.30y) / 0.04

Substitute this value of x in Equation 2:
(16 - 0.30y) / 0.04 + y = 200

Now, we can simplify and solve for y:

(16 - 0.30y + 0.04y) / 0.04 = 200
(16 - 0.26y) / 0.04 = 200

Multiply both sides by 0.04 to get rid of the denominator:
16 - 0.26y = 200 * 0.04
16 - 0.26y = 8

Subtract 16 from both sides:
-0.26y = -8
y = -8 / -0.26
y ≈ 30.77

Now, substitute the value of y back into Equation 2 to solve for x:
x + 30.77 = 200
x = 200 - 30.77
x ≈ 169.23

Therefore, approximately 169.23 pounds of whole milk and 30.77 pounds of cream should be mixed to form 200 pounds of milk for cream cheese.

The number of pounds of whole milk needed is approximately 169.23 pounds.
The number of pounds of cream needed is approximately 30.77 pounds.

169.23

30.77

.04x + .30(200-x) = .08(200)

x = 169.2 lbs whole milk
so, 30.8 lbs of cream.