A sugar solution was made by mixing 8qt of a 2% sugar solution and 6qt of a 51% sugar solution.  Find the concentration of the new mixture.

To find the concentration of the new mixture, we need to calculate the total amount of sugar in the solution and divide it by the total volume of the mixture.

### Step-by-Step Solution:

1. **Calculate the amount of sugar in each solution:**

   - For the 2% sugar solution:
     \[
     \text{Amount of sugar} = 8 \, \text{qt} \times \frac{2}{100} = 0.16 \, \text{qt}
     \]

   - For the 51% sugar solution:
     \[
     \text{Amount of sugar} = 6 \, \text{qt} \times \frac{51}{100} = 3.06 \, \text{qt}
     \]

2. **Calculate the total amount of sugar in the mixture:**

   \[
   \text{Total sugar} = 0.16 \, \text{qt} + 3.06 \, \text{qt} = 3.22 \, \text{qt}
   \]

3. **Calculate the total volume of the mixture:**

   \[
   \text{Total volume} = 8 \, \text{qt} + 6 \, \text{qt} = 14 \, \text{qt}
   \]

4. **Calculate the concentration of the new mixture:**

   \[
   \text{Concentration} = \left( \frac{\text{Total sugar}}{\text{Total volume}} \right) \times 100 = \left( \frac{3.22 \, \text{qt}}{14 \, \text{qt}} \right) \times 100
   \]

   \[
   \text{Concentration} = \left(0.23\right) \times 100 = 23\%
   \]

### Conclusion:

The concentration of the new mixture is **23%**.

Would you like more details or have any questions? 

Here are 5 related questions you might find interesting:

1. How would the concentration change if we used different volumes of each solution?
2. What if we mixed a 10% sugar solution instead of a 51% one?
3. How can you find the volume of a specific concentration needed to achieve a target mixture concentration?
4. How would you create a 10% solution by mixing a 2% and a 51% solution?
5. How does dilution affect the concentration of a solution?

**Tip:** Always ensure the units match when performing mixture calculations to avoid errors.

A sugar solution was made by mixing 8qt of a 2% sugar solution and 6qt of a 51% sugar solution. Find the concentration of the new mixture.

Learn how to calculate the concentration of a sugar solution made by mixing 8qt of a 2% solution with 6qt of a 51% solution. This problem covers key concepts in percentages, mixture problems, and the law of mixtures, 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