Two liquids of different densities (ρ1 = 1500 kg/m3, ρ2 = 500 kg/m3) are poured together into a 100 L tank, filling it. If the resulting density of the mixture is 800 kg/m3, find the respective masses of the liquids used.

Answer 1

I would be inclined to change the kg/m&3 to g/cc and change 100 L to cc but you aren't required to do that if you want to stay in the units and change 100 L to cubic meters.
So 1500 kg/m^3 = 1.5 g/cc
500 kg/m^3 = 0.500 g/cc
100L = 100,000 cc.

How much does the 100 L tank weigh?
100 x 0.800 g/cc = 80,000g
Let x = mass 1500 stuff.
Then 100,000-x = mass 500 stuff.
1.5g/cc * x + 0.500g/cc *(100,000-x) = 80,000 and solve for x and 100,000-x.