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Question

Difficulty: EasyWeighted Averages in Applied Contexts

A chemist prepares a mixture by combining 2020 liters of a 10%10\% saline solution with 3030 liters of a 20%20\% saline solution. What is the saline concentration, as a percentage, of the resulting mixture?

Answer: 16 %

Answer

The concentration of the resulting mixture is 16%16\%.
The total amount of pure saline in the mixture is 88 liters out of a total solution volume of 5050 liters. The overall concentration is 850×100%=16%\frac{8}{50} \times 100\% = 16\%.

Step-by-Step Solution

1
Calculate the total amount of pure saline solute contributed by both solutions.
20 L×0.10+30 L×0.20=2+6=8 liters20 \text{ L} \times 0.10 + 30 \text{ L} \times 0.20 = 2 + 6 = 8 \text{ liters}
The total solute is the sum of the solute amounts in each component solution.
2
Calculate the total volume of the combined mixture.
20+30=50 liters20 + 30 = 50 \text{ liters}
The combined volume is the sum of the individual volumes.
3
Compute the weighted average concentration of the mixture.
850=0.16=16%\frac{8}{50} = 0.16 = 16\%
The weighted average concentration equals total solute divided by total solution volume.

Key Concept

Weighted Average in Mixture Problems
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Topics

Weighted Averages in Applied Contexts

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