A dairy plant processes $1000\text{ kg}$ of whole milk containing $4.5\%$ fat into cream containing $40.0\%$ fat and skim milk containing $0.10\%$ fat. Assuming negligible mechanical spillage, the mass of cream produced in $\text{kg}$ is ________ (round off to 1 decimal place).
Answer Key:
110.3
Step-by-Step Solution & Explanation
Let $M_c$ be mass of cream and $M_s$ be mass of skim milk.
1. Total mass balance:
$M_c + M_s = 1000 \implies M_s = 1000 - M_c$
2. Fat balance:
$1000 \times 0.045 = M_c \times 0.40 + M_s \times 0.0010$
$45 = 0.40 M_c + 0.0010 (1000 - M_c) = 0.40 M_c + 1.0 - 0.0010 M_c$
$45 - 1.0 = 0.399 M_c \implies 44 = 0.399 M_c$
$M_c = \frac{44}{0.399} \approx 110.275\text{ kg} \approx 110.3\text{ kg}$