Let's break this problem down and solve it step by step.

Part 1: Completing the Table

The table represents a situation where a chemist is mixing two solutions to achieve a certain concentration of acid.

Liters of Solution	Percent Acid (as a decimal)	Liters of Pure Acid
10	0.04	0.04(10) = 0.4
x	0.12	0.12x
x + 10	0.08	0.08(x + 10)

So, the completed table is:

Liters of Solution	Percent Acid (as a decimal)	Liters of Pure Acid
10	0.04	0.4
x	0.12	0.12x
x + 10	0.08	0.08(x + 10)

Part 2: Determine the Amount of Solution to Add

To find the amount of the 12% acid solution to add (which is $x$ liters), we'll set up an equation based on the total liters of pure acid before and after mixing.

The equation is:

$\text{Pure acid from the first solution} + \text{Pure acid from the second solution} = \text{Total pure acid in the final mixture}$

Substituting the values from the table:

$0.4 + 0.12x = 0.08(x + 10)$

Now, solve for $x$:

$0.4 + 0.12x = 0.08x + 0.8$

Subtract $0.08x$ from both sides:

$0.4 + 0.04x = 0.8$

Subtract 0.4 from both sides:

$0.04x = 0.4$

Now, divide by 0.04:

$x = \frac{0.4}{0.04} = 10$

So, the chemist should add 10 liters of the 12% acid solution.

Summary

The chemist should add 10 liters of the 12% acid solution to achieve the desired concentration in the final mixture.

Would you like more details or have any questions? Here are five related questions that might interest you:

1. What is the final concentration if the chemist adds 15 liters of 12% acid solution instead?
2. How would the problem change if the initial solution was 20 liters at 4% acid?
3. Can you generalize a formula to find the amount of any percentage solution needed?
4. What would happen if the chemist wanted to achieve a 10% final concentration instead of 8%?
5. How can this process be applied to mixing solutions with different substances?

Tip: Always double-check your equation setup to ensure the concentrations and volumes are correctly represented before solving.