A company has:

Total assets that are the proportional to the square of the total liabilities.

The owner's equity is 249999.

Given that the total assets (A) are proportional to the square of the total liabilities (L), we can express this relationship as:

\[
A = k \cdot L^2
\]

where \(k\) is a constant of proportionality.

We also know the basic accounting equation:

\[
A = L + E
\]

where:
- \(A\) = total assets,
- \(L\) = total liabilities,
- \(E = 249,999\) = owner's equity.

We now have two equations:

1. \(A = k \cdot L^2\) (proportionality between assets and liabilities)
2. \(A = L + 249,999\) (accounting equation)

### To solve for the values of \(A\), \(L\), and \(k\):

1. Set the two equations for \(A\) equal to each other:

\[
k \cdot L^2 = L + 249,999
\]

This is a quadratic equation in \(L\). To solve for \(L\), we will use the quadratic formula.

Let me solve it for you.The solutions for \(L\) (total liabilities) in terms of the proportionality constant \(k\) are:

\[
L = \frac{1 - \sqrt{999996k + 1}}{2k} \quad \text{or} \quad L = \frac{\sqrt{999996k + 1} + 1}{2k}
\]

To find specific values for \(L\), \(A\), and \(k\), we would need more information about either total liabilities or total assets. Do you have any additional details regarding \(k\) or liabilities?

Would you like a step-by-step walkthrough of how to calculate these values based on an assumption for \(k\)? Let me know if you have more questions!

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Here are 5 follow-up questions:

1. Do you know the value of the constant of proportionality \(k\)?
2. What happens if the liabilities increase significantly?
3. Can we assume \(L\) is a positive value?
4. Would you like to see an example assuming \(k = 1\)?
5. How would changes in liabilities affect the equity?

**Tip:** In problems involving proportionality, identifying the constant can make solving much easier!

A company has: Total assets that are proportional to the square of the total liabilities. The owner's equity is 249999.

Explore how to solve for total liabilities using the proportional relationship between assets and liabilities squared in a company. This problem incorporates quadratic equations and the accounting equation, with an owner's equity of 249,999. Suitable for Grades 10-12.

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