You have 10 cups of a cleaning solution that is 10% white vinegar and 90% water. you want the mixture to be 50% white vinegar and 50% water. how many cups of white vinegar do you need to add to the mixture?

Let
x-->volume of white vinegar you need to add to the mixture (measured in cups)
then
the amount of the pure vinegar in the mixture will be > (10*0.1 + x) cups
the volume of liquid will be > 10 + x
the concentration equation is> [(10*0.1 + x)/(10+x)]=0.50multiply both sides by (10+x) and then simplify

(10*0.1 + x)=(10+x)*0.50> 1+x=5+0.50x> 0.50x=4
x=8

the answer is 
you need to add 8 of a cup of the pure vinegar to the mixture