In a direct variation, $y$ varies directly with $x$, meaning the relationship between $y$ and $x$ can be expressed as:

$y = kx$

where $k$ is the constant of variation.

Step 1: Find the constant of variation $k$

We are given that $y = 20$ when $x = 5$. Using this information, we substitute these values into the direct variation equation to find $k$:

$20 = k(5)$

Solving for $k$:

$k = \frac{20}{5} = 4$

Step 2: Use the constant $k$ to find $y$ when $x = 3$

Now that we know $k = 4$, we substitute this value into the direct variation equation and solve for $y$ when $x = 3$:

$y = 4(3) = 12$

Final Answer:

When $x = 3$, $y = 12$.

---

Would you like more details or further clarification on any step? Here are five related questions for practice:

1. If $y$ varies directly with $x$ and $y = 15$ when $x = 3$, what is $y$ when $x = 7$?
2. How do you know if two variables vary directly?
3. Find the constant of variation if $y = 30$ when $x = 10$.
4. If $y = 2x$, what is $y$ when $x = 8$?
5. What happens to $y$ as $x$ increases in a direct variation?

Tip: In direct variation problems, always find the constant first, then use it to solve for unknown values.