In a fruit juice processing plant, cane sugar is added to fresh orange juice containing $10^\circ\text{Brix}$ (soluble solids) to prepare a ready-to-serve cordial beverage of $15^\circ\text{Brix}$. To $170\text{ kg}$ of fresh juice, calculate the mass of pure dry sugar ($100^\circ\text{Brix}$) that must be added in $\text{kg}$.
Answer Key:
10
Step-by-Step Solution & Explanation
Let mass of sugar added be $S\text{ kg}$.
Initial solids in juice $= 170 \times 0.10 = 17\text{ kg}$.
Total solids in final blend $= 17 + S$.
Total mass of blend $= 170 + S$.
Desired Brix $= 15\% = 0.15$:
$\frac{17 + S}{170 + S} = 0.15$
$17 + S = 0.15(170 + S) = 25.5 + 0.15 S$
$0.85 S = 25.5 - 17 = 8.5$
$S = \frac{8.5}{0.85} = 10.0\text{ kg}$