Two syrups 30% and 20%: new concentration

200 g of sugar water at 30% concentration is combined with 300 g of sugar water at 20% concentration. What is the concentration of the blend?

Step-by-step

1. 200 × 30% = 60
   Solute in this portion
2. 300 × 20% = 60
   Solute in this portion
3. 60 + 60 = 120
   Total solute is unchanged during mixing
4. 120 ÷ 500 = 24%
   Concentration = solute ÷ total solution

Why it works

The dissolved sugar is conserved: the total sugar is the sum of each part's mass times its concentration, and the new concentration is that total sugar divided by the total mass.

Common mistakes

• Averaging 30% and 20% to get 25%.
• Using the total sugar but dividing by one part's mass only.

Related

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