John Loyd's Piggy Bank: A Math Problem Solving Journey
Introduction
John Loyd has a piggy bank and a saving strategy that involves gradual increases in his weekly deposits. This article provides a detailed solution to the puzzle of how much money John puts into his piggy bank during the sixth month. Along the way, we'll explore the arithmetic sequence and its application in practical scenarios like personal finance.
The Initial Amount and the Weekly Increase
John Loyd starts with 15 pesos in his piggy bank in the first week and plans to increase the weekly deposit by 15 pesos every week. This is a clear example of an arithmetic sequence in action. Let's break down the problem to find out how much John puts in his piggy bank during the sixth month, which includes weeks 17 to 24.
Week-by-Week Calculation
Week 1: 15 pesos
Week 2: 15 15 30 pesos
Week 3: 30 15 45 pesos
Week 4: 45 15 60 pesos
Week 5: 60 15 75 pesos
Week 6: 75 15 90 pesos
Continuing this pattern for 18 weeks up to the end of the first six months, we have:
Week 17: 345 15 360 pesos
Week 18: 360 15 375 pesos
Week 19: 375 15 390 pesos
Week 20: 390 15 405 pesos
Week 21: 405 15 420 pesos
Week 22: 420 15 435 pesos
Week 23: 435 15 450 pesos
Week 24: 450 15 465 pesos
Total for the Sixth Month
Now, let's sum the amounts deposited from Week 17 to Week 24:
360 375 735
735 390 1125
1125 405 1530
1530 420 1950
1950 435 2385
2385 450 2835
2835 465 3300
The total amount of money that John Loyd put in his piggy bank during the sixth month is 3300 pesos.
Additional Information and Real-World Application
This example perfectly illustrates the concept of an arithmetic sequence, where each term is derived by adding a fixed number to the previous term. In real-world applications, this concept is used in various situations like savings plans, investments, and financial planning.
Related Keywords and Concepts
Piggy Bank: A small savings box or container, usually for children.
Savings Calculation: The process of determining the total amount saved based on a series of deposits or withdrawals.
Arithmetic Sequence: A sequence of numbers in which each term after the first is obtained by adding a constant to the preceding one.
Tips for Saving: - Set a goal: Define what you want to save for. - Start small: Begin with a small, achievable deposit. - Be consistent: Make saving a regular part of your routine. - Track your progress: Keep a record of your savings to stay motivated. - Review and adjust: Regularly review your budget and adjust savings as needed.
Conclusion
John Loyd's piggy bank example is a hands-on application of arithmetic sequences and a great way to teach mathematics in a practical context. By understanding and implementing such strategies, individuals can effectively manage and grow their savings.