how much water should be evaporated from a gallon of a sugar-water solution that is 20% sugar to raise the concentration to 45% sugar

Let’s calculate the amount of water that needs to be evaporated to raise the concentration of sugar from 20% to 45% in a gallon of sugar-water solution.

### Step-by-step approach:

1. **Initial amount of sugar**:  
   A gallon of sugar-water solution contains 20% sugar.  
   Since there are 128 fluid ounces in a gallon, the amount of sugar is:
   \[
   \text{Sugar} = 20\% \times 128 \text{ ounces} = 0.20 \times 128 = 25.6 \text{ ounces of sugar.}
   \]

2. **Desired concentration of sugar**:  
   After evaporating water, we want the solution to be 45% sugar. Let \( x \) be the final volume of the solution after evaporation (in ounces).  
   At 45% concentration, the sugar content should still be 25.6 ounces, since no sugar is lost during evaporation. Thus:
   \[
   45\% \times x = 25.6
   \]
   \[
   0.45 \times x = 25.6
   \]
   Solving for \( x \):
   \[
   x = \frac{25.6}{0.45} \approx 56.89 \text{ ounces.}
   \]

3. **Amount of water to evaporate**:  
   Initially, we had 128 ounces of solution, and after evaporation, we want the final volume to be approximately 56.89 ounces. So, the amount of water to evaporate is:
   \[
   \text{Water to evaporate} = 128 - 56.89 \approx 71.11 \text{ ounces.}
   \]

### Conclusion:
Approximately **71.11 ounces of water** should be evaporated to raise the sugar concentration from 20% to 45%.

Do you want further details or have any questions?

Here are 5 related questions:
1. How do you calculate the sugar concentration if evaporation is not possible?
2. What happens if you evaporate too much water from the solution?
3. How does the volume of water affect the concentration change?
4. What would the final concentration be if only 50 ounces of water were evaporated?
5. How does temperature affect the evaporation rate in such a solution?

**Tip**: When evaporating water to concentrate a solution, only the solvent (water) is removed, leaving the solute (sugar) unchanged.

How much water should be evaporated from a gallon of a sugar-water solution that is 20% sugar to raise the concentration to 45% sugar?

Learn how to calculate the amount of water that must be evaporated from a gallon of a sugar-water solution to raise the concentration from 20% to 45%. This step-by-step solution involves using percentage formulas and algebraic equations to find the required evaporation amount. Suitable for students in Grades 8-10.

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