Question

Suppose `x` varies directly as both `y` and `z` (and `y` and `z` vary inversely with each other. If `x=6` when `y=6` and `z=123`, what is the value of `z` when `x=7` and `y-8`?

Answer 1

`z= 107 5/8`

Explanation:

For either "y directly as x and inversely as z" or "z directly as x and inversely as y":

`(y*z)/x = c` where `c` is a constant.

We are told `(x,y,z)=(6,6,123)` is a solution to this equation.

So
`color(white)("XXX")(cancel(6)*123)/cancel(6) = c`

If `x=7` and `y=8`, we have
`color(white)("XXXX")(8*z)/7 = 123`
`rArrcolor(white)("XXXXXXXXXXX")z = 861/8 = 107 5/8`