To prepare 600 mL of a 20% dextrose solution, how much of a 50% and a 5% dextrose solution are needed?

To determine the correct volumes of a 50% and a 5% dextrose solution needed to prepare a 600 mL solution of 20% dextrose, we use the concept of mass balance based on the percentages and volumes of each solution involved.

First, we denote the volume of the 50% solution as ( V_1 ) and the volume of the 5% solution as ( V_2 ). According to the problem, ( V_1 + V_2 = 600 ) mL.

Next, we calculate the total dextrose mass contributed by each solution. The mass of dextrose from the 50% solution is ( 0.50 \cdot V_1 ) and from the 5% solution is ( 0.05 \cdot V_2 ).

The desired concentration for the final 600 mL solution is 20%, which means that the total dextrose mass must equal ( 0.20 \cdot 600 = 120 ) grams.

Thus we set up the equation:

[ 0.50 \cdot V_1 + 0.05 \cdot V_2 = 120 \