A science teacher has a supply of 50% sugar solution and a supply of 80% sugar solution. How much of each solution should the teacher mix together to get 105 mL of 60% sugar solution for an experiment?
Let x be the amount of 50% sugar solution.
The amount of sugar in the 50% sugar solution is 0.5x.
The amount of sugar in the 80% sugar solution is 0.8(105 - x) since the total volume is 105 mL and x is the amount of 50% sugar solution.
The total amount of sugar in the mixture is 0.5x + 0.8(105 - x).
The total volume of the mixture is x + (105 - x) = 105 mL.
The 60% sugar solution is (0.5x + 0.8(105 - x))/105 = 60/100.
0.5x + 84 - 0.8x = 63.
-0.3x = -21.
x = 70 mL.
The teacher should mix 70 mL of the 50% sugar solution and 105 - 70 = <<105-70=35>>35 mL of the 80% sugar solution to get 105 mL of 60% sugar solution. Answer: \boxed{70,35}.