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. Understand that when mixing two solutions with different concentrations, the resulting concentration must lie between the two original concentrations. Here, the two solutions are 26% acid and 34% acid.
2. Recognize that the concentration of the mixture must be between 26% and 34%, inclusive, because mixing cannot produce a concentration lower than the smallest or higher than the largest concentration.
3. Check each given concentration option to see if it falls within the range 26% to 34%. The options are 24%, 30%, 31%, and 33%.
4. Identify that 24% is less than 26%, so it cannot be the concentration of the mixture since it is outside the possible range.
5. Conclude that the concentrations 30%, 31%, and 33% are all possible because they lie between 26% and 34%, but 24% is not possible.

Key Concepts

Mixture Problems and Weighted Averages

Mixture problems involve combining two or more solutions with different concentrations to find the concentration of the resulting mixture. The overall concentration is a weighted average based on the amounts and concentrations of each component. Understanding how to set up and solve these weighted averages is essential for determining possible mixture concentrations.

Range of Possible Concentrations

When mixing two solutions, the concentration of the mixture must lie between the concentrations of the individual solutions. This means the mixture concentration cannot be less than the lower concentration or greater than the higher concentration. Recognizing this range helps identify which concentrations are impossible.

Percent Concentration and Its Interpretation

Percent concentration represents the amount of acid per total solution, expressed as a percentage. Understanding how to interpret and compare these percentages is crucial for solving problems involving solution mixtures, as it allows for meaningful comparisons and calculations.