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To solve this problem, we can break it down step by step.

The key phrases are:
1. "Tú tienes la mitad de lo que tenías" (You have half of what you had).
2. "Después del negocio que hagas tendrás el triple de lo que tienes" (After the business deal, you will have triple what you currently have).
3. "Si tuvieras lo que tienes, tenías y tendrás, tendrías lo que yo tengo" (If you had what you currently have, what you had, and what you will have, you would have what I have).
4. "Yo tengo S/. 81 más de lo que tú tendrás" (I have 81 soles more than what you will have).

Let’s assign variables:
- Let \( x \) be what you currently have.
- You had \( 2x \) originally (because you have half of what you had).
- After the business, you will have \( 3x \) (triple what you currently have).

According to the problem:
- You would have \( x + 2x + 3x = 6x \) if you combined what you currently have, what you had, and what you will have.
- The amount I have is \( 6x + 81 \).

The total amount we have between the two of us is:
\[
6x + (6x + 81) = 12x + 81
\]

Now, let's check the options for \( x \). If \( x = 12 \), the total would be:
\[
12(12) + 81 = 144 + 81 = 225
\]

This is not in the options. Let’s try another value.

If \( x = 9 \), then:
\[
12(9) + 81 = 108 + 81 = 189
\]

This matches option **B) S/. 189**.

Thus, the answer is **B) S/. 189**.

Would you like further explanation on any step? Here are 5 related questions to consider:
1. How can you generalize problems involving proportions like this?
2. How do linear equations help solve real-world word problems?
3. What strategies can simplify multi-step problems like this?
4. Why is defining variables important in algebraic problems?
5. How do inequalities differ from equations in problem-solving?

**Tip**: Always break down complex word problems into smaller, manageable parts by translating phrases into algebraic expressions.

Tú tienes la mitad de lo que tenías y después del negocio que hagas tendrás el triple de lo que tienes. Si tuvieras lo que tienes, tenías y tendrás, tendrías lo que yo tengo, que es S/. 81 más de lo que tú tendrás. ¿Cuántos soles tenemos entre los dos?

Learn how to solve a linear word problem involving algebra and equations. The problem covers how to handle a business deal and calculate the total soles between two people, using linear equations. Suitable for Grades 8-10.

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