solutions question

Question

You need 200 mL of a 75% alcohol solution. On hand, you have a 50% alcohol mixture and a 90% alcohol mixture. How much of each mixture will you need to obtain the desired solution?

Answer 1

One approach to this problem is algebraic.    Let x = the needed volume of the 50% mixture and y = the needed volume of the 90% mixture.     Then

 

     .75   =  (.5 x + .9 y) /( x+y)       but also  x + y = 200   These equations can be reorganized as

 

    .5 x + .9 y = 150   and

      x + y       = 200

 

    This is two linear equations and two unknowns, so can be solved in a number of ways.  The solution is

   x =  75     ,     y = 125