Mathematical Problem Solving: Ravi's Chocolates

Today, we will explore a classic math problem presented through the lens of Ravi's chocolates. This problem not only hones our comprehension skills but also deepens our understanding of fractions and their practical applications. Let's delve into the problem and solve it step-by-step.

Introduction to the Problem

Imagine Ravi, a young boy who possesses an interesting collection of chocolates. Specifically, he has 3 dozen chocolates, which translates to 36 individual chocolates. Ravi then decides to share his chocolates with his neighbour, Reha, and his sister, distributing them in fractions. Our task is to determine how many chocolates Ravi is left with after making these distributions.

Step-by-Step Solution

Let's break down the problem into smaller, manageable parts and use a systematic approach to find our solution.

Step 1: Initial Distribution

Ravi gives away 1/3 of his chocolates to his neighbour. To calculate this, we perform the following calculation:

[ frac{1}{3} times 36 12 text{ chocolates} ]

After this distribution, Ravi is left with:

[ 36 - 12 24 text{ chocolates} ]

Step 2: Second Distribution

Ravi then gives away 1/6 of the remaining chocolates to Reha. The calculation for this step is:

[ frac{1}{6} times 24 4 text{ chocolates} ]

After this distribution, Ravi is left with:

[ 24 - 4 20 text{ chocolates} ]

Step 3: Third Distribution

Lastly, Ravi gives away 1/4 of the remaining chocolates to his sister. The calculation for this step is:

[ frac{1}{4} times 20 5 text{ chocolates} ]

After this distribution, Ravi is left with:

[ 20 - 5 15 text{ chocolates} ]

Therefore, by the end of these distributions, Ravi is left with 15 chocolates.

General Solution Approach

The problem can also be solved using a simplified approach by considering the total fraction of chocolates given away and then subtracting this from the initial amount. The total fraction given away can be calculated as:

[ frac{1}{3} frac{1}{6} frac{1}{4} frac{4}{12} frac{2}{12} frac{3}{12} frac{9}{12} frac{3}{4} ]

Therefore, the fraction of chocolates Ravi is left with is:

[ 1 - frac{3}{4} frac{1}{4} ]

Thus, the number of chocolates Ravi is left with is:

[ frac{1}{4} times 36 9 text{ chocolates} ]

Conclusion

In conclusion, through our step-by-step and simplified approaches, we have determined that Ravi is left with 9 chocolates after giving away part of his initial collection. This problem not only tests our understanding of fractions but also our ability to apply logical reasoning to solve real-life scenarios.