SOLUTION: If x varies inversely as y and y varies directly as z what is the relationship between x and z

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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