Question

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?

Answer 1

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