In chemistry class, Todd Corbin has 1 liter of a $$ 17 \% $$ sulfuric acid solution. How much of a $$ 12 \% $$ sulfuric acid solution must he mix with the 1 liter of $$ 17 \% $$ solution to make a $$ 14 \% $$ sulfuric acid solution? He must mix $$ \square $$ liters of a $$ 12 \% $$ sulfuric acid solution with the 1 liter of $$ 17 \% $$ solution to make a $$ 14 \% $$ sulfuric acid solution. (Type an integer, proper fraction, or mixed number.)

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To determine how much of a $$ 12\% $$ sulfuric acid solution Todd Corbin needs to mix with 1 liter of a $$ 17\% $$ solution to achieve a $$ 14\% $$ sulfuric acid solution, follow these steps:

1. **Set Up the Equation:**
   
   Let $$ x $$ be the number of liters of the $$ 12\% $$ solution needed.

The total amount of pure sulfuric acid from both solutions must equal the amount of pure sulfuric acid in the final mixture.

$$
   0.17 \times 1 + 0.12 \times x = 0.14 \times (1 + x)
   $$

2. **Simplify the Equation:**
   
   $$
   0.17 + 0.12x = 0.14 + 0.14x
   $$

3. **Solve for $$ x $$:**
   
   $$
   0.17 - 0.14 = 0.14x - 0.12x
   $$
   
   $$
   0.03 = 0.02x
   $$
   
   $$
   x = \frac{0.03}{0.02} = 1.5 \text{ liters}
   $$

So, Todd must mix **$$ \frac{3}{2} $$ liters** of a $$ 12\% $$ sulfuric acid solution with the 1 liter of $$ 17\% $$ solution to achieve the desired $$ 14\% $$ sulfuric acid solution.

**Answer:** $$ \dfrac{3}{2} $$ liters
Todd must mix $$ \frac{3}{2} $$ liters of a $$ 12\% $$ sulfuric acid solution with the 1 liter of $$ 17\% $$ solution to make a $$ 14\% $$ sulfuric acid solution.

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