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

$x = k \cdot y$

where $k$ is the constant of proportionality.

Step 1: Find the constant $k$

Given that $x = 35$ when $y = 7$, we can substitute these values into the equation:

$35 = k \cdot 7$

Solving for $k$:

$k = \frac{35}{7} = 5$

Step 2: Use the constant $k$ to find $y$ when $x = 25$

Now, we can use the equation $x = 5 \cdot y$ and substitute $x = 25$:

$25 = 5 \cdot y$

Solving for $y$:

$y = \frac{25}{5} = 5$

Thus, the value of $y$ when $x = 25$ is $y = 5$.

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Would you like further details or clarifications on any step?

Related Questions:

1. How would you solve if $x$ varies inversely with $y$?
2. What happens if both $x$ and $y$ vary directly with another variable?
3. How would the equation change if $x$ varied as the square of $y$?
4. Can you find $y$ if $x = 50$ under the same direct variation rule?
5. What if $y = 10$ and you needed to find $x$?

Tip:

For direct variation problems, remember that the ratio $\frac{x}{y}$ remains constant.