im stuck on this one can someone please help

Question

Find the volume of water which must be mixed with 20m3 of milk of specific gravity 1.032 in order to give a mixture of specific gravity 1.02.

Answer 1

One way to do this is as follows:

 

The final specific gravity (1.02) is the weighted average of the two specific gravities of the components.   The weights are the volume fractions.   Let f be the volume fraction (of the final volume) of the water to be added.   The volume fraction of the original milk is (1-f).     This leads to the equation:

 

     f (1.00) +  (1-f) 1.032 =  1.02.      {The specific gravity of pure water is 1.00}  

 

  This equation can be solved for f  yielding   f = .012/.032  =   3/8.    

 

    Thus the final mixture will be  3/8 water and 5/8 original milk  (by volume)

 

   Let V_tot be the volume of the mixture.   Then   (5/8) V_tot =  20 m³   This implies V_tot  =   32 m³ .

  So the volume of water to be added is  (3/8) 32  =  12 m³.