Question 1079187
x varies inversely as y leads to x = k/y


y varies directly as z leads to y = kz.


replacing y with kz in x = k/y leads to x = k/(kz)


simplifying that leads to x = 1/z


looks like z is the reciprocal of x.


this assumes that k is the same in both equations, as i believe it needs to be in order for the equations to work.


for example:


let x = 10 and y = 5.


we can solve for k in the first equation.


we get x = k/y becomes 10 = k/5.


solve for k to get k = 50.


now replace y with 5 and k with 50 in the second equation.


we get y = kz becomes 5 = 50 * z


solve for z to get z = 5/50 = 1/10


x was equal to 10
z is equal to 1/10


z is the reciprocal of x.


that's what i think is going on.
can't swear to it because i've never seen one like this before.
it does, however, seem reasonable.