Question

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
70 ML of the 50% solution and 35 ML of the 80% solution
35 ML of the 50% solution and 70 ML of the 80% solution
70 ML of the 50% solution and 70 ML of the 80% solution
35 ML of the 50% solution and 35 ML of the 80% solution

Answer 1

You can establish a system of two equation with two variables.

Varibles are:
V1 = volume of the 50% sugar solution
V2 = volumen of the 80% sugar solution

Equations:
Balance of sugar:

Sugar from 50% solution: 0.5*V1
Sugar from 80% solution: 0.8*V2
Sugar in the final solution (mix): 0.6 * 105 = 63

1) 0.5V1 + 0.8V2 = 63

Final volume = volume of 50% solution + volume of 80% solution

2) V1 + V2 = 105

From (2) V1 = 105 - V2

Substitue in (1)

0.5 (105 - V2) + 0.8 V2 = 63

52.5 - 0.5V2 + 0.8V2 = 63

0.3 V2 = 63 - 52.5

0.3 V2 = 10.5

V2 = 10.5/0.3
V2 = 35mL

V1 = 105 - 35 = 70 mL

Answer: 70 mL of the 50% solution and 35 mL of the 80% solution.