Ascience 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

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

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

For cyclohexane compounds drawn in a chair conformation:   -axial bonds are vertical  -equatorial bonds are parallel to two bonds within the ring.  thus, as i assume the chair conformation is drawn:   -the x group is in an axial position, as are the five other vertical bonds.  -three axial bonds are on the top face of the ring  -the other three axial bonds are on the bottom face  the position of the second substituent on each ring carbon is equatorial.  gauche groups must be on an adjacent carbon such as carbon 6 and carbon 2, and also gauche groups are rotated by 60 degrees relative to each other.  drawing the newman projections for c1–c2 and c1–c6 aids in visualizing the groups that are gauche to the y group on c1.  click this link and watch some academic videos that may you more understand the topic