Questions: A dairy farmer wants to mix a 65% protein supplement and a standard 15% protein ration to make 1200 pounds of a high-grade 30% protein ration. How many pounds of each should he use?

A dairy farmer wants to mix a 65% protein supplement and a standard 15% protein ration to make 1200 pounds of a high-grade 30% protein ration. How many pounds of each should he use?

Transcript text: A dairy farmer wants to mix a $65 \%$ protein supplement and a standard $15 \%$ protein ration to make 1200 pounds of a high-grade $30 \%$ protein ration. How many pounds of each should he use?

Solution

Solution Steps

Step 1: Define the equations based on the problem statement

We have two equations based on the given information:

Total weight equation: $x + y = W_f$
Protein balance equation: $P_s \cdot x + P_r \cdot y = P_f \cdot (x + y)$

Step 2: Solve the system of equations

Substitute $y = W_f - x$ into the protein balance equation and solve for $x$. This gives us $x = \frac{P_f \cdot W_f - P_r \cdot W_f}{P_s - P_r}$ and $y = W_f - x$.

Step 3: Calculation

After substituting the given values, we find that $x = 360$ pounds of the protein supplement and $y = 840$ pounds of the standard protein ration are needed.

Final Answer:

To achieve a 30% protein concentration in the final 1200 pounds mix, use 360 pounds of the high protein supplement and 840 pounds of the standard protein ration.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!