How much pure Alcohol should she add to the soultion?

Question

Paula has 60mm of a solution that is 46% alcohol. She plans to add pure alcohol until the solution is 79% alcohol.

Answer 1

Original volume = 60ml

Original % alcohol = 46%

therefore, amount of alcohol in 60ml solution = 0.46* 60=27.6 ml

 

Let x = amount of alcohol added.

New volume = (60+x)ml

new volume of alcohol = 27.6 + x

New % alcohol = 79%

 

(27.6+x)/(60+x) = 0.79

27.6+x = 0.79 (60+x)

            = 47.4 + 0.79x

Solving for x,

  x(1-0.79) = 47.4-27.6=19.8

  x(0.21) = 19.8

  x = 19.8/0.21 = 94.2857 ml

 

So, Paula needs to add 94.2857 ml of alcohol.

Answer 2

Let x = amount of pure alcohol that is added

 

Alcohol content of 46% solution = 0.46(60)

Alcohol content of pure alcohol = 1.00x

Alcohol content of mixture = 0.79(x+60)

 

0.46(60) + 1.00x = 0.79(x+60)

 

27.6 + x = 0.79x + 47.4

 

      0.21x = 19.8

 

             x = 94.285714