Solve each problem. Acid Mixture Suppose two acid solutions...

Solve each problem.
Acid Mixture Suppose two acid solutions are mixed. One is $26 \%$ acid and the other
is $34 \%$ acid. Which one of the following concentrations cannot possibly be the concentration of the mixture?
A. $24 \%$
B. $30 \%$
C. $31 \%$
D. $33 \%$

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Key Concepts

Weighted Average

The weighted average is a key concept in mixture problems whereby each component's contribution to the overall property is proportional to its amount. In concentration problems, the final percent is calculated as a 'weighted' mix of the concentrations of the individual solutions, which inherently means that the resulting mixture’s concentration must lie between the lowest and highest percent values provided.

Mixture Problems

Mixture problems involve combining substances with different properties, such as concentrations, to obtain a mixture whose overall property is a weighted average of its components. This requires an understanding of how the ratios of the individual components affect the overall characteristic of the mixture.

Boundary Values in Mixtures

When mixing solutions of different concentrations, the resulting concentration must fall between the concentrations of the pure components. This is because the final concentration is calculated as a convex combination of the given concentrations, meaning it cannot exceed the maximum or fall below the minimum of the components.

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