Solving the Oranges Puzzle: A Step-by-Step Guide to Calculating Quantity

Are you a fan of logic puzzles and mathematical challenges? In today's article, we will explore a common riddle involving Mrs. Li and a handful of oranges. We will break down the problem systematically to uncover the mystery of how many oranges Mrs. Li initially bought.

Introduction to the Problem

Mrs. Li bought a certain number of oranges. Throughout the day, she gave away some of these oranges in a specific sequence. By the end of the day, she had six oranges left. The challenge is to determine how many oranges Mrs. Li initially purchased.

Step-by-Step Solution

We will represent the total number of oranges Mrs. Li bought as x.

Giving to Her Sister

Mrs. Li first gave away 1/2 of her oranges to her sister.

Mathematically, this can be expressed as:

Oranges left x - (1/2) * x (1/2) * x

Giving to Her Neighbor

She then gave away 1/4 of the remaining oranges to her neighbor.

The oranges given to her neighbor can be calculated as:

Oranges given to neighbor (1/4) * (1/2) * x 1/8 * x

Oranges left after giving to her neighbor:

Oranges left (1/2) * x - (1/8) * x 4/8 * x - 1/8 * x 3/8 * x

Giving to Her Children

Next, she gave away 3/5 of the remaining oranges to her children.

The oranges given to her children can be calculated as:

Oranges given to children 3/5 * (3/8) * x 9/40 * x

Oranges left after giving to her children:

Oranges left (3/8) * x - (9/40) * x

To subtract these, we need a common denominator. The least common multiple of 8 and 40 is 40:

(3/8) * x (15/40) * x

Now, subtract the two fractions:

Oranges left (15/40) * x - (9/40) * x (6/40) * x (3/20) * x

Final Amount

It is given that she has 6 oranges left at the end:

(3/20) * x 6

By solving for x:',

x 6 * (20/3) 40

Hence, Mrs. Li initially bought 40 oranges.

Checking the Answer

Let's check if the answer (40 oranges) is correct:

1. Mrs. Li gives half (20/40 20 oranges) to her sister.

2. She then gives 1/4 of the remaining (1/4 * 20 5 oranges) to her neighbor.

3. She gives 3/5 of the remaining (3/5 * 15 9 oranges) to her children.

Subtracting these, she has 6 oranges left:

(20 - 5 - 9) 6

This confirms that our solution is correct.

Conclusion

Here is a step-by-step guide to solving this logic puzzle. Whether you are a math enthusiast or a student looking to improve your problem-solving skills, practicing such riddles can greatly enhance your logical and analytical abilities.

There are countless ways to solve puzzles like this one. Choosing the most systematic approach ensures the accuracy of your answer. If you face similar problems in the future, taking a methodical approach can help you approach them with confidence and precision.