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Question 1079187: If x varies inversely as y and y varies directly as z what is the relationship between x and z
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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