Andy, Luke, And Tina Share Some Sweets In The Ratio \[$1: 6: 14\$\].Tina Gives \[$\frac{3}{7}\$\] Of Her Sweets To Andy.Tina Then Gives \[$12 \frac{1}{2} \%\$\] Of The Rest Of Her Sweets To Luke.Tina Says, Now All Three Of Us
Introduction
In this article, we will delve into a mathematical puzzle involving the sharing of sweets among three individuals, Andy, Luke, and Tina. The puzzle revolves around the ratio in which they share the sweets and the subsequent transactions that take place among them. We will explore the mathematical concepts and problem-solving strategies required to unravel the mystery of the sweet sharing conundrum.
The Initial Sweet Sharing Ratio
The initial sweet sharing ratio among Andy, Luke, and Tina is given as 1:6:14. This means that for every 1 sweet that Andy receives, Luke receives 6 sweets, and Tina receives 14 sweets. To better understand this ratio, let's consider a common multiple of the numbers 1, 6, and 14. A suitable common multiple is 42, which is the least common multiple (LCM) of 1, 6, and 14.
Using the common multiple of 42, we can express the initial sweet sharing ratio as follows:
- Andy receives 1/42 of the total sweets
- Luke receives 6/42 of the total sweets
- Tina receives 14/42 of the total sweets
Tina's Gift to Andy
Tina decides to give 3/7 of her sweets to Andy. To calculate the number of sweets Tina gives to Andy, we need to find 3/7 of the total sweets that Tina initially receives. Since Tina receives 14/42 of the total sweets, we can calculate the number of sweets she gives to Andy as follows:
Tina's sweets = (14/42) × 42 = 14 Sweets given to Andy = (3/7) × 14 = 6
So, Tina gives 6 sweets to Andy.
Tina's Remaining Sweets
After giving 6 sweets to Andy, Tina is left with:
Tina's remaining sweets = 14 - 6 = 8
Tina's Gift to Luke
Tina decides to give 12 1/2% of her remaining sweets to Luke. To calculate the number of sweets Tina gives to Luke, we need to find 12 1/2% of the remaining sweets. First, let's convert the percentage to a decimal:
12 1/2% = 12.5% = 0.125
Now, we can calculate the number of sweets Tina gives to Luke as follows:
Sweets given to Luke = (0.125) × 8 = 1
So, Tina gives 1 sweet to Luke.
The Final Sweet Sharing Ratio
After the transactions, the final sweet sharing ratio among Andy, Luke, and Tina is as follows:
- Andy receives 1 + 6 = 7 sweets
- Luke receives 6 + 1 = 7 sweets
- Tina receives 14 - 6 - 1 = 7 sweets
The final sweet sharing ratio is 1:1:1, indicating that all three individuals now have an equal share of the sweets.
Conclusion
In this article, we explored a mathematical puzzle involving the sharing of sweets among three individuals, Andy, Luke, and Tina. We used the initial sweet sharing ratio and subsequent transactions to unravel the mystery of the sweet sharing conundrum. The problem required us to apply mathematical concepts such as ratios, percentages, and fractions to arrive at the final solution. The final sweet sharing ratio of 1:1:1 indicates that all three individuals now have an equal share of the sweets.
Mathematical Concepts
The following mathematical concepts were applied in this article:
- Ratios: The initial sweet sharing ratio was given as 1:6:14, and we used the common multiple of 42 to express the ratio.
- Percentages: We converted the percentage 12 1/2% to a decimal and used it to calculate the number of sweets Tina gives to Luke.
- Fractions: We used fractions to represent the number of sweets Tina gives to Andy and the number of sweets Tina gives to Luke.
Problem-Solving Strategies
The following problem-solving strategies were employed in this article:
- Breaking down complex problems into smaller, manageable parts
- Using mathematical concepts and formulas to solve the problem
- Applying logical reasoning and critical thinking to arrive at the final solution
Real-World Applications
The mathematical concepts and problem-solving strategies applied in this article have real-world applications in various fields, such as:
- Finance: Understanding ratios and percentages is essential in finance, where investors need to analyze financial data and make informed decisions.
- Business: Calculating percentages and fractions is crucial in business, where companies need to manage inventory, calculate profits, and make strategic decisions.
- Science: Mathematical concepts such as ratios and percentages are used in scientific research to analyze data and draw conclusions.
Introduction
In our previous article, we explored the sweet sharing conundrum, a mathematical puzzle involving the sharing of sweets among three individuals, Andy, Luke, and Tina. We used the initial sweet sharing ratio and subsequent transactions to unravel the mystery of the sweet sharing conundrum. In this article, we will answer some frequently asked questions (FAQs) related to the sweet sharing conundrum.
Q: What is the initial sweet sharing ratio among Andy, Luke, and Tina?
A: The initial sweet sharing ratio among Andy, Luke, and Tina is 1:6:14. This means that for every 1 sweet that Andy receives, Luke receives 6 sweets, and Tina receives 14 sweets.
Q: How do we calculate the number of sweets Tina gives to Andy?
A: To calculate the number of sweets Tina gives to Andy, we need to find 3/7 of the total sweets that Tina initially receives. Since Tina receives 14/42 of the total sweets, we can calculate the number of sweets she gives to Andy as follows:
Tina's sweets = (14/42) × 42 = 14 Sweets given to Andy = (3/7) × 14 = 6
Q: What percentage of her remaining sweets does Tina give to Luke?
A: Tina gives 12 1/2% of her remaining sweets to Luke. To calculate the number of sweets Tina gives to Luke, we need to find 12 1/2% of the remaining sweets. First, let's convert the percentage to a decimal:
12 1/2% = 12.5% = 0.125
Now, we can calculate the number of sweets Tina gives to Luke as follows:
Sweets given to Luke = (0.125) × 8 = 1
Q: What is the final sweet sharing ratio among Andy, Luke, and Tina?
A: After the transactions, the final sweet sharing ratio among Andy, Luke, and Tina is as follows:
- Andy receives 1 + 6 = 7 sweets
- Luke receives 6 + 1 = 7 sweets
- Tina receives 14 - 6 - 1 = 7 sweets
The final sweet sharing ratio is 1:1:1, indicating that all three individuals now have an equal share of the sweets.
Q: What mathematical concepts are used in the sweet sharing conundrum?
A: The following mathematical concepts are used in the sweet sharing conundrum:
- Ratios: The initial sweet sharing ratio was given as 1:6:14, and we used the common multiple of 42 to express the ratio.
- Percentages: We converted the percentage 12 1/2% to a decimal and used it to calculate the number of sweets Tina gives to Luke.
- Fractions: We used fractions to represent the number of sweets Tina gives to Andy and the number of sweets Tina gives to Luke.
Q: What problem-solving strategies are used in the sweet sharing conundrum?
A: The following problem-solving strategies are used in the sweet sharing conundrum:
- Breaking down complex problems into smaller, manageable parts
- Using mathematical concepts and formulas to solve the problem
- Applying logical reasoning and critical thinking to arrive at the final solution
Q: What are the real-world applications of the mathematical concepts used in the sweet sharing conundrum?
A: The mathematical concepts used in the sweet sharing conundrum have real-world applications in various fields, such as:
- Finance: Understanding ratios and percentages is essential in finance, where investors need to analyze financial data and make informed decisions.
- Business: Calculating percentages and fractions is crucial in business, where companies need to manage inventory, calculate profits, and make strategic decisions.
- Science: Mathematical concepts such as ratios and percentages are used in scientific research to analyze data and draw conclusions.
Conclusion
In this article, we answered some frequently asked questions related to the sweet sharing conundrum. We hope that this Q&A article has provided a better understanding of the mathematical concepts and problem-solving strategies used in the sweet sharing conundrum. If you have any further questions or need clarification on any of the concepts, please feel free to ask.