How much 50% sugar syrup can you make if you have x grams of sugar ? HELP I WILL GIVE 13PT

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