A tank holds 120 liters of a chemical solution. Currently, the solution has a strength of $$ 70 \% $$. How much of this should be drained and replaced with $$ 100 \% $$ solution to get a final strength of $$ 90 \% $$ ? How many liters should be drained and replaced with $$ 100 \% $$ solution? liters

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To determine how much of the solution should be drained and replaced to achieve a final strength of $$ 90\% $$, let's follow these steps:

1. **Initial Setup:**
   - **Total Volume:** $$ 120 $$ liters
   - **Initial Strength:** $$ 70\% $$
   - **Desired Strength:** $$ 90\% $$

2. **Calculate the Initial Amount of Pure Chemical:**
   $$
   \text{Initial pure chemical} = 0.70 \times 120 = 84 \text{ liters}
   $$

3. **Let $$ x $$ be the amount to drain and replace.**

4. **After Draining $$ x $$ Liters:**
   - **Volume Removed:** $$ x $$ liters
   - **Pure Chemical Removed:** $$ 0.70 \times x $$ liters
   - **Pure Chemical Remaining:** $$ 84 - 0.70x $$ liters

5. **Adding $$ x $$ Liters of $$ 100\% $$ Solution:**
   - **Pure Chemical Added:** $$ x $$ liters
   - **Total Pure Chemical After Replacement:**
     $$
     84 - 0.70x + x = 84 + 0.30x \text{ liters}
     $$

6. **Set Up the Equation for Desired Strength:**
   $$
   84 + 0.30x = 0.90 \times 120 = 108 \text{ liters}
   $$

7. **Solve for $$ x $$:**
   $$
   0.30x = 108 - 84
   $$
   $$
   0.30x = 24
   $$
   $$
   x = \frac{24}{0.30} = 80 \text{ liters}
   $$

**Conclusion:**
You should drain and replace **80 liters** of the solution with $$ 100\% $$ chemical to achieve the desired $$ 90\% $$ strength.

**Answer:** 80\ \text{liters}
You should drain and replace **80 liters** of the solution with $$ 100\% $$ chemical to achieve a final strength of $$ 90\% $$.

A tank holds 120 liters of a chemical solution. Currently, the solution has a strength of \( 70 \% \). How much of this should be drained and replaced with \( 100 \% \) solution to get a final strength of \( 90 \% \) ? How many liters should be drained and replaced with \( 100 \% \) solution? liters

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