$x$ varies directly as $p$. If $x=32$ when $p=16$, find $x$ when $p$ is 20 . \[ x= \]

Step 1 ：The problem states that $x$ varies directly as $p$. This means that $x$ and $p$ are directly proportional to each other. The formula for direct variation is $x = kp$, where $k$ is the constant of variation.

Step 2 ：We can find the value of $k$ using the given values of $x$ and $p$. Given that $x=32$ when $p=16$, we can substitute these values into the formula to get $32 = k*16$. Solving for $k$ gives us $k = 2.0$.

Step 3 ：Now that we have the value of $k$, we can find the value of $x$ when $p$ is 20. Substituting these values into the formula gives us $x = 2.0*20$.

Step 4 ：Solving for $x$ gives us $x = 40.0$.

Step 5 ：Final Answer: \(\boxed{40}\)