Math Problem Statement

resolver ejercicio

Un padre, al morir, decide en su testamento que se reparta S/60,000 en forma proporcional a las edades de sus 3 hijos que son 20; 25 y 30 años. Sin embargo, los hijos deciden repartirse la herencia en forma equitativa. Calcule cuánto dinero adicional recibirá el menor de los hermanos.

Solution

The problem seems to be with the language settings for text extraction. I will now manually proceed with solving the exercise based on what is visible in the uploaded image. Here's the problem:

A father has left an inheritance of S/60,000 to be distributed proportionally among his three children, aged 20, 25, and 30 years. However, the children decide to split the inheritance equally. We are asked to calculate how much additional money the youngest child (aged 20) will receive under the new arrangement.

Solution:

  1. Proportional Distribution: The proportional split should be based on their ages. Let's denote the ages of the children as:

    • Age of the first child = 20
    • Age of the second child = 25
    • Age of the third child = 30

    The total age sum is 20+25+30=7520 + 25 + 30 = 75.

    So, the inheritance is split in the ratio 2075\frac{20}{75}, 2575\frac{25}{75}, and 3075\frac{30}{75} for each child respectively.

    The inheritance for each child under the proportional split is:

    • First child: 2075×60,000\frac{20}{75} \times 60,000
    • Second child: 2575×60,000\frac{25}{75} \times 60,000
    • Third child: 3075×60,000\frac{30}{75} \times 60,000
  2. Equal Distribution: If they decide to split the inheritance equally, each child would receive 60,0003=20,000\frac{60,000}{3} = 20,000.

  3. Additional Money for the Youngest Child: To find how much more the youngest child will receive in the equal distribution compared to the proportional distribution, we calculate the difference between the two distributions.

Let me compute the exact values next.The youngest child will receive an additional S/4,000 under the equal distribution compared to the proportional distribution based on their ages.

Would you like more details on any step or further clarifications?

Here are 5 related questions for further exploration:

  1. How would the distribution change if there were four children?
  2. What if the inheritance had to be divided based on a different criterion, such as education level?
  3. How does the proportional distribution benefit or disadvantage the younger sibling?
  4. Could the children decide on another distribution method that isn't proportional or equal?
  5. How could inflation affect the value of an inheritance over time?

Tip: When splitting assets proportionally, it's important to first clarify the basis (e.g., age, need, contribution) to ensure fairness among all parties involved.

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Math Problem Analysis

Mathematical Concepts

Proportional Distribution
Arithmetic

Formulas

Proportional Share = (Age / Total Age Sum) * Total Inheritance
Equal Share = Total Inheritance / Number of Children
Additional Amount = Equal Share - Proportional Share

Theorems

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Suitable Grade Level

Grades 10-12