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The problem involves mixing two solutions to obtain a final concentration.

We have:
- Solution A, concentration \( N/10 \)
- Solution B, concentration \( N/2 \)
- Final solution with concentration \( N/5 \)
- Total volume required: 2 liters

We can use the concept of dilution:

Let:
- \( V_A \) be the volume of solution A (concentration \( N/10 \))
- \( V_B \) be the volume of solution B (concentration \( N/2 \))
- The final volume is \( V_A + V_B = 2 \) liters.

We also need to satisfy the concentration requirement:
\[
\frac{V_A}{10} + \frac{V_B}{2} = \frac{2}{5}
\]

### Solving the system of equations:

1. \( V_A + V_B = 2 \)
2. \( \frac{V_A}{10} + \frac{V_B}{2} = \frac{2}{5} \)

Let's solve this system.

First, multiply the second equation by 10 to eliminate the denominators:
\[
V_A + 5V_B = 4
\]

Now solve the system:
1. \( V_A + V_B = 2 \)
2. \( V_A + 5V_B = 4 \)

By subtracting the first equation from the second:
\[
( V_A + 5V_B ) - ( V_A + V_B ) = 4 - 2
\]
\[
4V_B = 2
\]
\[
V_B = 0.5
\]

Now, substitute \( V_B = 0.5 \) into \( V_A + V_B = 2 \):
\[
V_A + 0.5 = 2
\]
\[
V_A = 1.5
\]

### Solution:
The correct volumes are:
- \( V_A = 1.5 \) liters of solution A
- \( V_B = 0.5 \) liters of solution B

Thus, the answer is **C) 1.5 L - 0.5 L**.

Would you like further details on the solution process or have any other questions?

Here are 5 related questions:
1. How would the result change if the final concentration were \( N/4 \)?
2. What happens if you mix solutions of different acids, not the same acid?
3. How can you calculate the concentration of a mixed solution from multiple solutions?
4. How would you approach if one solution were more concentrated than \( N/2 \)?
5. Can you use the same method for solids mixed in water?

**Tip**: Always verify your final concentration by recalculating after mixing to avoid mistakes in lab settings.

Una solución A de un ácido es N/10 y otra solución B del mismo ácido es N/2. ¿Qué volúmenes (L) de las soluciones deberán mezclarse respectivamente para obtener 2 litros de solución que sea N/5?

Learn how to mix two solutions of an acid with concentrations N/10 and N/2 to get 2 liters of a solution with concentration N/5. This problem involves concepts of dilution and algebra, including key formulas for solving chemical concentration problems. Suitable for students in Grades 9-12.

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