Answer:
S = x / 0.5
Step-by-step explanation:
Sugar Syrup percent to make: 50%
grams of sugar = x
If we want to make a sugar syrup then we need to make a solution that consists of soluble and solvent. Soluble is sugar and solvent is water. Given that we have x grams of sugar so lets say we have y of water. Lets say S represents the mass of this solution of sugar and water, we need to mix x grams of sugar with y grams of water so it becomes:
S = x + y
Now if you need to make 50% sugar syrup this means 1/2 of the total mass will be sugar and 1/2 would be water.
S = x + y ____ (1)
The percentage of sugar syrup is 50% . So this means 1/2= 0.5 of the total mass of sugar is needed to make a sugar syrup.
So representing the above logic into an equation we get:
50% = (mass of solute/mass of solution) * 100 ____ (2)
where
mass of solution = mass of solvent + mass of solute
From (1)
x = mass of solute
y = mass of solvent
S = mass of solution
So S = x + y
So using (1) and (2)
50% = (x/S) * 100%
50%/100% = x/S
50% = x/S _____ (3)
It can also be represented as:
0.5 = x/S
This means 1/2 = 0.5 of the total mass is sugar, and 1/2 =0.5 is water
So if we have x grams of sugar then amount of 50% sugar syrup that we can make using (3) is:
S = x / 50%
It can also be represented as S = x/0.5
