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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