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

Transcript text: What is the percentage of Feed $B$ to be used in the ration?

Solution

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.

Step 1: Define the Problem

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 $0.12$.

Step 2: Set Up the Equations

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

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

Step 3: Solve the Equations

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 $: \[ y = 1 - (-1) = 2 \]

Step 4: Interpret the Solution

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

$\boxed{\text{Not feasible}}$

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