How many pound of cream containing 12% butterfat must be added to 1800lb.of milk containing 2% butterfat to obtain milk having 3% butterfat?
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To solve this problem, we need to determine how many pounds of cream containing 12% butterfat must be added to 1800 pounds of milk containing 2% butterfat in order to obtain milk containing 3% butterfat.
Let's break down the problem into smaller steps:
Step 1: Set up the equation
We can use the concept of the mixture equation, which states that the amount of a certain component in the mixture is proportional to the amount of that component in each individual ingredient.
Let's assume the weight of cream to be added is "x" pounds. Therefore, the weight of milk will remain constant at 1800 pounds.
The equation can be written as follows:
0.12x + 0.02 * 1800 = 0.03 * (x + 1800)
The left side of the equation represents the butterfat content in the cream and the milk, while the right side represents the desired butterfat content in the final mixture.
Step 2: Solve the equation
Let's solve the equation to find the value of "x".
0.12x + 36 = 0.03x + 54
Rearranging the equation:
0.12x - 0.03x = 54 - 36
0.09x = 18
Divide both sides of the equation by 0.09:
x = 18 / 0.09
x = 200
Therefore, 200 pounds of cream containing 12% butterfat must be added to 1800 pounds of milk containing 2% butterfat to obtain milk with 3% butterfat.