Question 154167
The following fact is used to set up the equation:
The amount of the pure alcohol before mixing must be equal to the amount of the pure alcohol after mixing.
So
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The solution before mixing: 1L of 50% solution
The amount of alcohol before mixing is 50%*1
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The solution after mixing: 1+x liters of 20% solution
The amount of alcohol after mixing is 20%*(1+x)
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So the equation is:
50%*1 = 20%(1+x)

Solving for x, we have
50 = 20(1+x)   (multiply both sides by 100)
50 = 20 + 20x
30 = 20x
30/20 = x
1.5 = x