Tomatoes and Shop Stoppers: A Mathematical Journey

Imagine a bustling market where countless shops offer the same product: tomatoes. This intriguing mathematical problem revolves around a shopping trip taken by Mary Joy. Let's break down the challenge she faces as she moves from shop to shop, collecting tomatoes along the way.

Problem Statement

The problem presented asks us to determine how many tomatoes Mary Joy collects in a series of ten shops, given that she buys 2 tomatoes in the first shop and then an additional 2 tomatoes in every subsequent shop she passes by.

The Mathematics Behind the Problem

1. Initial Collection

At the first shop, Mary Joy buys a straightforward 2 tomatoes. This forms the basis of her collection, initiating the mathematical sequence.

2. Pattern Recognition

For each shop after the first, Mary Joy adds 2 more tomatoes to her collection. This pattern is crucial in understanding the total number of tomatoes collected over the 10 shops.

3. Calculation

Let's calculate the total number of tomatoes Mary Joy collects:

Total Collection: The number of tomatoes in the first shop is 2. In each of the subsequent 9 shops, she gets an additional 2 tomatoes. This can be mathematically expressed as:

2 (2x9)

This simplifies to:

2 18 20 tomatoes

Further Explanation

1. Sequence and Series

The sequence of Mary's tomato collection can be described as an arithmetic sequence where the first term (a1) is 2 and the common difference (d) is 2. The sum of the sequence can be calculated using the formula for the sum of the first n terms of an arithmetic series:

Sn n/2 * (2a1 (n-1) * d)

Substituting the values n 10, a1 2, and d 2, we get:

S10 10/2 * (2*2 (10-1)*2)

S10 5 * (4 18)

S10 5 * 22 20

2. Shopping Trip Strategy

This problem not only reinforces mathematical concepts but also provides insight into practical shopping strategies. Mary Joy's approach is efficient and ensures a consistent addition to her collection.

Conclusion

Through this problem, we see how basic arithmetic and sequence calculations can be applied in real-life scenarios. Whether it's a shopping trip or a more complex problem, understanding these mathematical principles can help simplify and solve daily challenges.