Answer:
32 liters
Explanation:
We must create a set of two equations to model the current situation and what we want as our end outcome and set the equations equal to each other and solve for the unknown liter quantity of the solution.
Solving:
[tex]\section*{}Let \( x \) be the liters of the 30\% solution to be added.\section*{Total Volume:}The total volume after mixing will be:\[V = 40 + x \text{ liters}\][/tex]
[tex]\section*{Equation Creation:}The total amount of acid from both solutions must equal the amount of acid in the final solution.1. \textbf{Acid from 12\% solution:} \[ 0.12 \times 40 = 4.8 \text{ liters of acid} \]2. \textbf{Acid from 30\% solution:} \[= 0.30x \text{ liters of acid} ~(\text{We are solving for x}) \]3. \textbf{Total acid in the final solution:} \[ = 0.20(40 + x)[/tex]
[tex]\section*{Equation Solving:}Combining the acid amounts, we have:\[4.8 + 0.30x = 0.20(40 + x)\]\[4.8 + 0.30x = 8 + 0.20x\]\\Subtract \( 0.20x \) from both sides:\[4.8 - 8 = 0.20x - 0.30x\]\[-3.2 = -0.10x\]\[x = \frac{-3.2}{-0.10} = \boxed{32\text{ liters}}\][/tex]
Therefore, Wendy should use 32 liters of the 30% acid solution.