Questions: What is the percentage of Feed B to be used in the ration?

Solution Steps

The problem seems to involve mixing different feeds to achieve a certain percentage composition. To solve this, we can use the concept of weighted averages or a system of equations to determine the percentage of Feed B needed in the mixture. We will assume that the percentages given are the protein content of each feed and that we need to find the proportion of Feed B in the final mixture.

We are tasked with finding the percentage of Feed B needed in a mixture to achieve a target protein percentage. Given:

• Feed A has a protein content of \(20\%\) or \(0.20\).
• Feed B has a protein content of \(16\%\) or \(0.16\).
• The target protein content for the mixture is \(12\%\) or \(0.12\).

We set up the following system of equations based on the problem:

1. \( x + y = 1 \) (The total percentage of the mixture must be \(100\%\))
2. \( 0.20x + 0.16y = 0.12 \) (The weighted average of the protein content must equal the target percentage)

Solving the system of equations:

• From equation 1: \( y = 1 - x \)
• Substitute \( y = 1 - x \) into equation 2: \[ 0.20x + 0.16(1 - x) = 0.12 \] Simplifying: \[ 0.20x + 0.16 - 0.16x = 0.12 \] \[ 0.04x = -0.04 \] \[ x = -1 \]
• Substitute \( x = -1 \) back into \( y = 1 - x \): \[ y = 1 - (-1) = 2 \]

The solution \( x = -1 \) and \( y = 2 \) indicates an inconsistency in the problem setup, as percentages cannot be negative or exceed \(100\%\). This suggests that achieving a \(12\%\) protein content with the given feeds is not feasible.

Final Answer