You use the idea that
#"concentration=amount of substance/volume of solution"#
In symbols:
#c=n/v#
This means that
#n=cxxv#
In questions like this the total amount of substance does not change so we can write:
#(60xxV_(60))+(15xxV_(15))=30xx650" "color(red)((1))#
We also know that the total volume is #650"ml"# so we can also write:
#V_(60)+V_(15)=650" "color(red)((2))#
So we have set up two simultaneous equations. There are two equations and two unknowns so they can be solved easily.
From #color(red)((2))# we can rearrange:
#V_(60)=(650-V_(15))#
We now substitute this expression for #V_(60)# into #color(red)((1))rArr#
#60(650-V_(15))+15V_(15)=19500#
#:.39000-60V_(15)+15V_(15)=19500#
#:.39000-45V_(15)=19500#
#:.45V_(15)=39000-19500=19500#
#:.V_(15)=19500/45=433.3"ml"#
From #color(red)((2))# we know that:
#V_(60)+V_(15)=650#
#:.V_(60)=650-V_(15)#
#:.V_(60)=650-433.3=216.6"ml"#
