Distribute € 390 Between Two People So That One Of Them Takes 30 Percent Of What The Other Takes
Problem Statement
We are given a total amount of € 390 that needs to be distributed between two people. The condition is that one person should receive 30% of what the other person receives. We need to find the amount each person should receive.
Step 1: Define the Variables
Let's assume the amount received by the first person is x. Since the second person receives 30% of what the first person receives, the amount received by the second person is 0.3x.
Step 2: Set Up the Equation
The total amount to be distributed is € 390. Therefore, the sum of the amounts received by both people should be equal to € 390. We can set up the equation as follows:
x + 0.3x = 390
Step 3: Simplify the Equation
Combine like terms:
1.3x = 390
Step 4: Solve for x
To solve for x, divide both sides of the equation by 1.3:
x = 390 / 1.3
x = 300
Step 5: Find the Amount Received by the Second Person
Now that we have found the value of x, we can find the amount received by the second person by multiplying x by 0.3:
Amount received by the second person = 0.3x = 0.3(300) = 90
Conclusion
Therefore, the first person should receive € 300 and the second person should receive € 90.
Example Use Case
This problem can be applied to real-life scenarios such as:
- Distributing a bonus among employees, where one employee receives a higher percentage of the bonus than the others.
- Allocating a budget among team members, where one team member receives a higher percentage of the budget than the others.
Tips and Variations
- To make the problem more challenging, you can increase the percentage received by the second person or add more people to the distribution.
- To make the problem easier, you can decrease the percentage received by the second person or reduce the total amount to be distributed.
Mathematical Concepts
This problem involves the following mathematical concepts:
- Algebraic equations
- Simplifying expressions
- Solving for variables
- Percentage calculations
Real-World Applications
This problem has real-world applications in various fields such as:
- Business: Distributing bonuses, allocating budgets, and making financial decisions.
- Finance: Calculating interest rates, investment returns, and loan payments.
- Economics: Analyzing market trends, calculating GDP, and making economic forecasts.
Conclusion
Q: What is the total amount to be distributed?
A: The total amount to be distributed is € 390.
Q: What is the condition for distributing the amount?
A: The condition is that one person should receive 30% of what the other person receives.
Q: How do we define the variables in this problem?
A: Let's assume the amount received by the first person is x. Since the second person receives 30% of what the first person receives, the amount received by the second person is 0.3x.
Q: What is the equation we set up to solve this problem?
A: The equation is x + 0.3x = 390.
Q: How do we simplify the equation?
A: We combine like terms to get 1.3x = 390.
Q: How do we solve for x?
A: To solve for x, we divide both sides of the equation by 1.3: x = 390 / 1.3.
Q: What is the value of x?
A: The value of x is 300.
Q: How do we find the amount received by the second person?
A: We multiply x by 0.3 to get the amount received by the second person: 0.3(300) = 90.
Q: What is the amount received by each person?
A: The first person receives € 300 and the second person receives € 90.
Q: What are some real-world applications of this problem?
A: This problem has real-world applications in various fields such as:
- Business: Distributing bonuses, allocating budgets, and making financial decisions.
- Finance: Calculating interest rates, investment returns, and loan payments.
- Economics: Analyzing market trends, calculating GDP, and making economic forecasts.
Q: What mathematical concepts are involved in this problem?
A: This problem involves the following mathematical concepts:
- Algebraic equations
- Simplifying expressions
- Solving for variables
- Percentage calculations
Q: How can we make this problem more challenging?
A: We can increase the percentage received by the second person or add more people to the distribution.
Q: How can we make this problem easier?
A: We can decrease the percentage received by the second person or reduce the total amount to be distributed.
Q: What are some tips for solving this problem?
A: Some tips for solving this problem include:
- Read the problem carefully and understand the condition.
- Define the variables clearly.
- Set up the equation correctly.
- Simplify the equation and solve for the variable.
Q: What are some common mistakes to avoid when solving this problem?
A: Some common mistakes to avoid when solving this problem include:
- Not reading the problem carefully.
- Not defining the variables clearly.
- Not setting up the equation correctly.
- Not simplifying the equation and solving for the variable.
Conclusion
In conclusion, distributing € 390 between two people so that one of them takes 30 percent of what the other takes involves solving an algebraic equation. By following the steps outlined in this article, you can find the amount each person should receive. This problem has real-world applications and involves various mathematical concepts.