how many liters of a 10% dextrose should be mixed with a 20Liter of a 15% solution to obtain a 12% dextrose solution?

Let's solve the problem step by step.

### Given:
- We need to mix a 10% dextrose solution with a 15% dextrose solution.
- The volume of the 15% solution is 20 liters.
- The final solution should be 12% dextrose.

### Let:
- \( x \) be the volume of the 10% dextrose solution to be mixed (in liters).

### Set up the equation based on the concentration of dextrose:
The amount of dextrose in the 10% solution: \( 0.10x \)  
The amount of dextrose in the 20 liters of 15% solution: \( 0.15 \times 20 \)

The total amount of dextrose in the final solution: \( 0.12 \times (x + 20) \)

### Equation:
\[
0.10x + 0.15 \times 20 = 0.12 \times (x + 20)
\]

### Solve the equation:

1. Expand and simplify the equation:
\[
0.10x + 3 = 0.12x + 2.4
\]

2. Subtract \( 0.10x \) from both sides:
\[
3 = 0.02x + 2.4
\]

3. Subtract 2.4 from both sides:
\[
0.6 = 0.02x
\]

4. Solve for \( x \):
\[
x = \frac{0.6}{0.02} = 30
\]

### Conclusion:
You need to mix **30 liters** of the 10% dextrose solution with 20 liters of the 15% solution to obtain a 12% dextrose solution.

Would you like more details on any step or have any questions?

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Here are 5 related questions to deepen your understanding:

1. How would the problem change if the target concentration were 14% instead of 12%?
2. How can you check if the final solution indeed has 12% dextrose?
3. What would happen if you mixed equal parts of 10% and 15% dextrose solutions?
4. How would the equation change if you had a different amount of the 15% solution?
5. What if you were using a 5% dextrose solution instead of a 10% one?

**Tip:** When dealing with mixture problems, setting up the equation properly with the correct concentrations is crucial to finding the right solution.

How many liters of a 10% dextrose solution should be mixed with 20 liters of a 15% solution to obtain a 12% dextrose solution?

Learn how to solve a mixture problem by calculating how many liters of a 10% dextrose solution should be mixed with 20 liters of a 15% solution to get a 12% solution. This problem covers algebraic concepts and linear equations, suitable for Grades 9-10.

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