S.O.S. Mathematics CyberBoard

Here's a question in my textbook that I wanted to solve for the past few days, "Suppose x varies inversely with y and y varies inversely with z. How does x vary with z?"

I thought it would be something like: x = a/y & y = a/z. I solved for y in the first equation and got that y = a/x. Then I went back and plugged that back into the second equation and then got a/x=a/z, then I solved for x, and found out that x = z.

But my teacher told me that it's wrong, any help would be much appreciated.

The constants do not have to be the same, so you should end up with x = kz for some k, in other words x and z vary directly.

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