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.