Question

You need a 70% alcohol solution. On hand, you have a 135 mL of a 20% alcohol mixture. You also have 85% alcohol mixture. How much of the 85% mixture will you need to add to obtain the desired solution

Answer 1

To obtain the desired solution:

450 mL of 85% alcohol solution is needed to obtain the desired solution.  

Calculation:

Let x be the amount of the 85% alcohol required

The volume of the resulting 70% alcohol solution will then be = x + 135 ml

135 mL of the 20% alcohol solution contains the amount of "pure" alcohol is =  0.20×135 mL.

The 85% alcohol solution contains x mL of "pure" alcohol = 0.85× x mL.

The total amount of the "pure" alcohol is the sum

=  0.20×135 + 0.85× x mL.

It should be equal to the amount of the "pure" alcohol in the mixture, which is = 0.70× (x+135) ml.

So, your "pure alcohol" equation is,  

=  0.85× x + 0.20×135 = 0.70× (x+135)

Simplify and solve it for x:

0.85x + 0.20×135 = 0.70x + 0.70×135,

0.85x - 0.70x = 0.70×135 - 0.20×135,

0.15x = 67.5

x = 67.5/0.15

= 450mL.

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