Since $y$ varies directly with $x$, we can express this relationship as:

$y = kx$

where $k$ is the constant of proportionality.

Step 1: Find $k$

Using the given values $y = 15$ when $x = 20$, we substitute into the equation:

$15 = k(20)$

$k = \frac{15}{20} = \frac{3}{4}$

Step 2: Verify for $x = 400$, find $y$

We substitute $x = 400$ into the equation:

$y = \frac{3}{4} \times 400$

$y = 300$

So, when $x = 400$, $y$ should be 300, not 4.
There seems to be an inconsistency in the given problem. Would you like to clarify any values?

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Here are some related questions for practice:

1. If $y$ varies directly with $x$ and $y = 10$ when $x = 5$, find $y$ when $x = 50$.
2. If $a$ varies directly with $b$ and $a = 24$ when $b = 8$, find $b$ when $a = 60$.
3. The circumference $C$ of a circle varies directly with its diameter $d$. If $C = 31.4$ when $d = 10$, find $C$ when $d = 25$.
4. The force $F$ required to move an object varies directly with its mass $m$. If $F = 20$ Newtons when $m = 5$ kg, find $F$ when $m = 12$ kg.
5. If $z$ varies directly with $w$ and $z = 18$ when $w = 6$, find $w$ when $z = 30$.

Tip:

To solve direct variation problems, always find the constant of proportionality first and use it to make calculations easier!