How many liters of pure alcohol must be added to 10 liters o

How many liters of pure alcohol must be added to 10 liters of a 30% solution to obtain a 50 % solution?

Solution

Pure alcohol =100
X=number of liters of pure alcohol
X+10=final volume of 50% solution
Convert perscentages to decimal
100%=100/100=1 30%=30/100=.3 50%=50/100=.5

The total volume is constant before and after.

1(x)+10(.30)=(x+10).5
Use the distributive property
x+3=.5x +5
subtract 3 from both sides
subtract .5x from both sides
.5x=2
Divide both sides by .5
x=4
Therefore 4 liters of pure alcohol need to be added. Let\'s check our answer
4(1)+10(.3)=14(.5)
4+3=7