solution should she​ add?
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Part 1
Complete the table.
Liters of Solution
Percent Acid 
​(as a​ decimal)
Liters of Pure Acid
10
0.04
  
0.04 left parenthesis 10 right parenthesis
x
0.12
  
0.12 x
  
x plus 10
0.08
  
0.08 left parenthesis x plus 10 right parenthesis
​(Do not​ simplify.)
Part 2
The chemist should add 
  
4 liters of 12​% acid solution.
​(Simplify your answer. Type an integer or a​ decimal

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.

Learn how to solve solution mixing problems to calculate acid concentrations. This problem involves mixing different acid solutions to achieve a specified concentration. Step-by-step solution included.

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