How do I figure out the following question:

A close rectangular box has a surface area of 1000 square centimeters. Its length is twice its width and its height is 6 times its width, what is the volume?

From your second piece of information

\frac{1}{2}l = \frac{1}{6}h = w

From your first information

2lw + 2hw + 2hl = 1000

Now using the first equation to convert everythign into w

2w(2w) + 2w(6w) + 2(2w)(6w) = 1000

4w^2 + 12w^2 + 24w^2 = 1000

40w^2 = 1000

Now you can solve for w, then you can use the first equation I stated to get the length and height.

Then use:

V = lhw

to find your final volume.

Let me know if you need more help.