Question

Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case for 75% syrup?

Answer 1

0.16 lbs of water added to obtain 0.5 lbs of syrup.

Explanation:

Given : Ella has 0.5 lbs of sugar.

To find : How much water should she add to make the following concentrations?

Solution :

Mass of sugar = 0.5 lbs

Concentration = 75%

Formula used to find the mass of the solution,

`\text{Mass of the solution}=\frac{\text{mass of sugar}*100}{\text{concentration}}`

`\text{Mass of the solution}=(0.5*100)/(75)`

`\text{Mass of the solution}=(50)/(75)`

`\text{Mass of the solution}=0.66`

Mass of water = mass of solution - mass of sugar

Mass of water = 0.66- 0.5

Mass of water = 0.16

Therefore, 0.16 lbs of water added to obtain 0.5 lbs of syrup.

Answer 2

To answer this item, let x be the amount of water. The concentration (in % sugar) of the solution is calculated by dividing the amount of sugar by the total amount. That is,

C = (S/ (S + x))(100%)

Substituting the known values to the equation,

75 = ((0.5/(0.5 + x))(100%)

The value of x from the equation is 0.167.

Answer: 0.167 lbs of water