Let f be amount of 43% and s be amount of 16%...
s+f=90, f=90-s
(.16s+.43f)/90=.25 using f found above we get:
(.16s+.43(90-s))/90=.25
.16s+38.7-.43s=22.5
-.27s=-16.2
s=60, and since f=90-s, f=30
So the chemist will need to mix 60ml of 16% solution with 30ml of 43% solution to create 90ml of a 25% solution.