https://file.aiquickdraw.com/mathbot/file/1726192853762tj3ro9l2.jpg

The problem states:

"4 qt. of a 40% sugar solution was mixed with 12 qt. of pure water. What is the concentration of the mixture?"

### Step-by-Step Solution:

1. **Volume of Sugar in the Initial Solution:**
   - You have 4 quarts of a 40% sugar solution.
   - The amount of sugar in this solution is:
     \[
     \text{Sugar in 4 qt solution} = 0.40 \times 4 = 1.6 \text{ qt of sugar}.
     \]

2. **Volume of Pure Water Added:**
   - You are mixing this solution with 12 quarts of pure water (0% sugar).
   - The amount of sugar in pure water is 0, so no additional sugar is added.

3. **Total Volume of the Mixture:**
   - The total volume of the mixture is:
     \[
     \text{Total Volume} = 4 \, \text{qt} + 12 \, \text{qt} = 16 \, \text{qt}.
     \]

4. **Concentration of the Mixture:**
   - The total sugar remains 1.6 quarts, and the total volume is now 16 quarts.
   - The concentration of the sugar in the mixture is:
     \[
     \text{Concentration} = \frac{\text{Total Sugar}}{\text{Total Volume}} = \frac{1.6}{16} = 0.10 = 10\%.
     \]

### Final Answer:
The concentration of the mixture is **10%** sugar.

Would you like more details or further clarification? Here are some related questions to explore:

1. What would happen if more pure water was added to the solution?
2. How would the concentration change if instead of pure water, another sugar solution was added?
3. What is the mathematical formula for mixing solutions of different concentrations?
4. How would the concentration change if you started with a 20% sugar solution instead of 40%?
5. Can this method be applied to other substances like salt or alcohol?

**Tip:** When mixing solutions, the total amount of solute (in this case, sugar) stays the same unless more solute is added or removed.

4 qt. of a 40% sugar solution was mixed with 12 qt. of pure water. What is the concentration of the mixture?

Learn how to find the concentration of sugar in a mixture when 4 quarts of a 40% sugar solution are combined with 12 quarts of pure water. This step-by-step solution explains how to calculate concentration by using percentages and basic algebra. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation