$z$ varies inversely as $t$. If $z$ is 35 when $t$ is 15 , find $z$ when $t$ is 105 .
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Step 1 ：The problem states that $z$ varies inversely as $t$. This means that the product of $z$ and $t$ is a constant. We can write this relationship as $zt = k$, where $k$ is the constant of variation.

Step 2 ：We can find the value of $k$ using the given values of $z$ and $t$. Given that $z$ is 35 when $t$ is 15, we can substitute these values into the equation $zt = k$ to get $35 \times 15 = k$. Therefore, $k = 525$.

Step 3 ：Once we have $k$, we can find the value of $z$ when $t$ is 105. We substitute $k = 525$ and $t = 105$ into the equation $zt = k$ to get $z = \frac{k}{t} = \frac{525}{105}$.

Step 4 ：Solving the above equation gives $z = 5$.

Step 5 ：Final Answer: The value of $z$ when $t$ is 105 is \(\boxed{5}\).