Question

John Accidentally pured too much water in his syrup and has 10 oz of 20% syrup. How much water should he evaporate to obtain 50% syrup?

Answer 1

John needs to evaporate 6 ounces of water from his 10 oz of 20% syrup solution to achieve a 50% syrup concentration.

Step-by-step explanation:

John currently has 10 oz of a 20% syrup solution and wishes to evaporate water to obtain a 50% syrup solution. To calculate how much water he should evaporate, we need to apply the concept of concentration and mass balance.

First, we calculate the current amount of syrup in the solution:

• Amount of syrup = 20% of 10 oz = 0.20 × 10 oz = 2 oz

To have a 50% syrup solution, syrup should be 50% of the total weight. Let 'w' be the final weight of the solution after evaporation:

• 2 oz (amount of syrup) = 50% of w

From this, we can derive:

• w = 2 oz / 0.50
• w = 4 oz

Therefore, to have a 50% syrup solution, the total weight of the solution should be 4 oz. We subtract this from the original 10 oz to find the amount of water to evaporate:

• Amount of water to evaporate = Initial weight - Final weight
• Amount of water to evaporate = 10 oz - 4 oz
• Amount of water to evaporate = 6 oz

John needs to evaporate 6 ounces of water to obtain a 50% syrup solution.