Subtopic: Material and energy balances in food processing systems
Question Statement:
Using the Pearson Square method, $2000\text{ kg}$ of market milk containing $3.0\%$ milk fat is to be prepared by blending whole buffalo milk ($6.0\%$ fat) with skim milk ($0.5\%$ fat). The mass of buffalo milk required in $\text{kg}$ is ________ (round off to 1 decimal place).
Answer Key:
909.1
Step-by-Step Solution & Explanation
Let $M_b$ be the mass of buffalo milk and $M_s$ be the mass of skim milk.
1. Total mass balance: $M_b + M_s = 2000 \implies M_s = 2000 - M_b$
2. Fat balance:
$M_b (0.06) + (2000 - M_b)(0.005) = 2000 (0.03)$
$0.06 M_b + 10.0 - 0.005 M_b = 60.0$
$0.055 M_b = 50.0$
$M_b = \frac{50.0}{0.055} = 909.09\text{ kg} \approx 909.1\text{ kg}$