300 grams of sugar solution has 40% of sugar in it. How much sugar should be…

Step-by-Step Solution

To solve this, we must ensure the amount of sugar represents the desired percentage of the total weight of the solution.

1. Analyze the Initial State:

   • Total initial solution = 300 grams

   • Sugar concentration = 40%

   • Initial sugar amount = 0.40 * 300 = 120 grams

   • Initial water/other components amount = 300 - 120 = 180 grams

2. Analyze the Target State:

   • Let 'x' be the grams of sugar to be added.

   • New sugar amount = 120 + x

   • New total solution weight = 300 + x

   • Target sugar concentration = 55%

3. Set up the Equation:

   • (New sugar amount) / (New total solution weight) = 0.55

   • (120 + x) / (300 + x) = 0.55

4. Solve for x:

   • 120 + x = 0.55 * (300 + x)

   • 120 + x = 165 + 0.55x

   • x - 0.55x = 165 - 120

   • 0.45x = 45

   • x = 45 / 0.45

   • x = 100 grams.