Ann-Marie Bought Apples. She Kept One-third For Herself And Gave The Rest To 4 Friends. Each Friend Got 2 Apples.How Many Apples Did Ann-Marie Buy?

Mar 13, 2025 by ADMIN 148 views

**Solving the Apple Puzzle: A Math Problem for the Ages**

Introduction

Mathematics is a fascinating subject that surrounds us in every aspect of life. From the simplest calculations to complex algorithms, math is an essential tool for problem-solving and critical thinking. In this article, we will delve into a classic math problem that involves fractions, division, and basic arithmetic operations. Our goal is to find out how many apples Ann-Marie bought, given that she kept one-third for herself and distributed the rest among her four friends.

The Problem Statement

Ann-Marie bought apples and decided to share them with her friends. She kept one-third of the apples for herself and gave the remaining two-thirds to four friends. Each friend received two apples. How many apples did Ann-Marie buy in total?

Breaking Down the Problem

To solve this problem, we need to break it down into smaller, manageable parts. Let's start by identifying the key information:

Ann-Marie kept one-third of the apples for herself.
She gave two-thirds of the apples to four friends.
Each friend received two apples.

Using Algebra to Represent the Problem

Let's use algebra to represent the problem. We can let x be the total number of apples Ann-Marie bought. Since she kept one-third of the apples for herself, the number of apples she kept is x/3. The remaining two-thirds of the apples were given to four friends, so the number of apples each friend received is (2x/3) ÷ 4 = x/6.

Setting Up the Equation

Since each friend received two apples, we can set up the equation:

x/6 = 2

Solving the Equation

To solve for x, we can multiply both sides of the equation by 6:

x = 2 × 6 x = 12

Conclusion

Therefore, Ann-Marie bought 12 apples in total. This solution makes sense, as one-third of 12 is 4, and two-thirds of 12 is 8. Since each friend received two apples, the total number of apples given to the four friends is 8, which is consistent with our solution.

Real-World Applications

This problem may seem simple, but it has real-world applications in various fields, such as:

Cooking: When cooking for a group of people, you need to calculate the amount of ingredients required. This problem can help you determine the total amount of ingredients needed.
Shopping: When buying items in bulk, you need to calculate the total cost. This problem can help you determine the total cost of the items.
Science: In scientific experiments, you need to calculate the amount of materials required. This problem can help you determine the total amount of materials needed.

Tips and Tricks

Here are some tips and tricks to help you solve similar problems:

Use algebra: Algebra is a powerful tool for solving math problems. Use variables to represent unknown values and set up equations to solve for the unknowns.
Break down the problem: Break down the problem into smaller, manageable parts. This will help you identify the key information and set up the equation.
Check your units: Make sure your units are consistent. In this problem, we used apples as the unit of measurement. Make sure you use the correct unit of measurement for the problem you are solving.

Conclusion

In conclusion, solving the apple puzzle requires a combination of algebra, fractions, and basic arithmetic operations. By breaking down the problem into smaller parts and using algebra to represent the unknown values, we can set up an equation and solve for the total number of apples Ann-Marie bought. This problem has real-world applications in various fields, and by using algebra and breaking down the problem, we can solve similar problems with ease.

Introduction

In our previous article, we solved the apple puzzle by using algebra and fractions to determine the total number of apples Ann-Marie bought. In this article, we will answer some frequently asked questions related to the problem.

Q: What if Ann-Marie had given the apples to 5 friends instead of 4?

A: If Ann-Marie had given the apples to 5 friends instead of 4, the number of apples each friend received would be (2x/3) ÷ 5 = x/15. Since each friend received two apples, we can set up the equation:

x/15 = 2

To solve for x, we can multiply both sides of the equation by 15:

x = 2 × 15 x = 30

Therefore, if Ann-Marie had given the apples to 5 friends instead of 4, she would have bought 30 apples.

Q: What if Ann-Marie had kept two-thirds of the apples for herself instead of one-third?

A: If Ann-Marie had kept two-thirds of the apples for herself instead of one-third, the number of apples she kept would be 2x/3. The remaining one-third of the apples would be given to the four friends. Since each friend received two apples, we can set up the equation:

(2x/3) ÷ 4 = 2

To solve for x, we can multiply both sides of the equation by 12:

2x = 2 × 12 2x = 24

x = 24 ÷ 2 x = 12

Therefore, if Ann-Marie had kept two-thirds of the apples for herself instead of one-third, she would have bought 12 apples.

Q: What if Ann-Marie had given the apples to 3 friends instead of 4?

A: If Ann-Marie had given the apples to 3 friends instead of 4, the number of apples each friend received would be (2x/3) ÷ 3 = x/9. Since each friend received two apples, we can set up the equation:

x/9 = 2

To solve for x, we can multiply both sides of the equation by 9:

x = 2 × 9 x = 18

Therefore, if Ann-Marie had given the apples to 3 friends instead of 4, she would have bought 18 apples.

Q: Can I use a calculator to solve this problem?

A: Yes, you can use a calculator to solve this problem. However, it's always a good idea to understand the underlying math concepts and to use algebra to represent the problem. This will help you to develop problem-solving skills and to understand the solution.

Q: How can I apply this problem to real-life situations?

A: This problem can be applied to real-life situations such as:

Cooking: When cooking for a group of people, you need to calculate the amount of ingredients required. This problem can help you determine the total amount of ingredients needed.
Shopping: When buying items in bulk, you need to calculate the total cost. This problem can help you determine the total cost of the items.
Science: In scientific experiments, you need to calculate the amount of materials required. This problem can help you determine the total amount of materials needed.

Conclusion

Additional Resources

If you want to learn more about algebra and fractions, here are some additional resources:

Algebra tutorials: Websites such as Khan Academy and Mathway offer algebra tutorials and practice problems.
Fraction tutorials: Websites such as Math Open Reference and Fraction Calculator offer fraction tutorials and practice problems.
Math books: Books such as "Algebra for Dummies" and "Fractions for Dummies" offer comprehensive explanations and practice problems.

Practice Problems

Here are some practice problems to help you apply the concepts learned in this article:

Problem 1: Tom has 15 apples and wants to share them equally among 5 friends. How many apples will each friend receive?
Problem 2: Sarah has 24 apples and wants to keep 1/3 of them for herself. How many apples will she give to her 4 friends?
Problem 3: John has 18 apples and wants to give 2/3 of them to his 3 friends. How many apples will each friend receive?

I hope this article has been helpful in answering your questions and providing additional resources for learning algebra and fractions.