If fresh apple juice contains 10% solids, what would be the solid content of a concentrates that would yield single-strength juice after diluting one part of the concentrate with three parts of water? Assume that the densities are constant and are equal to the density of water.
To solve this problem, we need to use the equation:
% solids in concentrate = (% solids in single-strength juice) x (volume reduction ratio)
Volume reduction ratio = 1 / (dilution factor)
Dilution factor = total volume of single-strength juice / volume of concentrate
For this problem, the % solids in single-strength juice is 10%, and the dilution factor is 1:3, since we are diluting one part of concentrate with three parts of water. Therefore:
Dilution factor = (1+3) / 1 = 4
Volume reduction ratio = 1 / 4 = 0.25
% solids in concentrate = 10% x 0.25 = 2.5%
Therefore, the solid content of the concentrate would be 2.5% to yield single-strength juice after diluting one part of the concentrate with three parts of water.
To find the solid content of the concentrate, we need to understand the concept of dilution.
Dilution is the process of reducing the concentration (in this case, the solid content) of a solution by adding more solvent (in this case, water).
Given that one part of the concentrate is diluted with three parts of water, we can determine the overall solids content by using the concept of mass conservation.
Let's assume that we have 1 liter of the concentrate. Since the density of water is the same as that of the concentrate, the volume of the diluted solution would be 1 + 3 = 4 liters.
The total amount of solid content in the concentrate before dilution can be calculated as follows:
Total solid content in the concentrate = (volume of concentrate) * (solid content percentage)
= 1 liter * 10%
= 0.1 liters
Since the diluted solution is 4 liters, we divide the total solid content by the new volume to get the solid content in the diluted solution:
Solid content of diluted solution = (total solid content) / (volume of diluted solution)
= 0.1 liters / 4 liters
= 0.025 liters
So, the solid content of the concentrate that would yield single-strength juice after dilution would be 0.025 liters.
To find the solid content of the concentrate that would yield single-strength juice after dilution, we can use the following steps:
Step 1: Determine the solid content in the single-strength juice.
Since the fresh apple juice contains 10% solids, it means that 100 - 10 = 90% of the juice is water. This translates to a water content of 90% in the single-strength juice.
Step 2: Determine the dilution ratio.
The dilution ratio is given as one part concentrate to three parts water. This means that the total volume after dilution will be four parts (1 part concentrate + 3 parts water).
Step 3: Determine the water content in the diluted juice.
Since water is diluted at a ratio of 3:4 (3 parts water out of 4 total parts), we can calculate the water content in the diluted juice:
Water content in diluted juice = total water content / total parts
= (3 parts water / 4 total parts) * 100%
= 75% water in the diluted juice.
Step 4: Determine the solid content in the diluted juice.
Since the water content in the diluted juice is 75%, the remaining percentage must be the solid content:
Solid content in diluted juice = 100% - water content in diluted juice
= 100% - 75%
= 25%.
Therefore, the solid content in the concentrate should be 25% in order to yield single-strength juice after diluting one part of the concentrate with three parts of water.