Solve each problem. 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%

Verified step by step guidance

1. insert step 1> Identify the range of possible concentrations for the mixture. Since one solution is 26% acid and the other is 34% acid, the concentration of the mixture must be between these two values.
2. insert step 2> Analyze each option to see if it falls within the range of 26% to 34%.
3. insert step 3> Check option A: 24%. Since 24% is less than 26%, it cannot be the concentration of the mixture.
4. insert step 4> Check option B: 30%. Since 30% is between 26% and 34%, it can be a possible concentration.
5. insert step 5> Check options C and D: 31% and 33%. Both are within the range of 26% to 34%, so they can be possible concentrations.

Key Concepts

Weighted Average

The concentration of a mixture can be understood as a weighted average of the concentrations of the individual components. In this case, the percentages of acid in the two solutions (26% and 34%) will determine the possible concentrations of the resulting mixture based on the proportions in which they are mixed.

Concentration Range

When mixing two solutions, the concentration of the resulting mixture must fall within the range defined by the concentrations of the two solutions. For the given problem, the minimum concentration is 26% and the maximum is 34%, meaning any concentration outside this range is impossible.

Linear Combination

The concept of linear combination applies here, as the final concentration of the mixture can be expressed as a linear combination of the concentrations of the two solutions. This means that the resulting concentration can be calculated based on the ratio of the volumes of the two solutions mixed, leading to specific possible concentrations.