https://file.aiquickdraw.com/mathbot/file/1725477985894fjtgwpio.jpg

The problem in the image states:

"The variable is proportional to \( x \), and \( y = 25 \) when \( x = 125 \). Determine \( y \) when \( x = 50 \)."

### Solution:

When a variable \( y \) is directly proportional to \( x \), it can be written as:
\[
y = kx
\]
where \( k \) is the constant of proportionality.

Given:
- \( y = 25 \) when \( x = 125 \).

We can find the value of \( k \) using these values:
\[
25 = k \times 125
\]
\[
k = \frac{25}{125} = \frac{1}{5}
\]

Now, to find \( y \) when \( x = 50 \), we use the equation:
\[
y = \frac{1}{5} \times 50
\]
\[
y = 10
\]

### Final Answer:
\( y = 10 \) when \( x = 50 \).

Would you like more details on this solution or have any other questions? Here are some related questions:

1. How would the equation change if \( y \) was inversely proportional to \( x \)?
2. What happens to \( y \) if \( x \) doubles?
3. How can you express the proportional relationship between \( y \) and \( x \) using a graph?
4. What if \( y \) was proportional to the square of \( x \)? How would you solve it?
5. Can you determine the constant \( k \) using a different set of \( y \) and \( x \) values?

**Tip:** When dealing with proportional relationships, always solve for the constant of proportionality first, as it simplifies finding the value of the variable for any given input.

The variable is proportional to x, and y = 25 when x = 125. Determine y when x = 50.

Learn how to solve a direct proportion problem where y is proportional to x, and y = 25 when x = 125. This problem involves finding the value of y when x = 50 using the formula y = kx, making it suitable for students in Grades 6-8.

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