Solving a Mathematical Puzzle: Roses and Carnations in a Florist's Shop

This article addresses a challenging puzzle involving a florist's shop, where an initial inventory of roses and carnations undergoes a series of changes. The puzzle requires a detailed analysis and step-by-step solution to determine the number of roses sold. Let's break down the problem and solve it systematically.

Initial Conditions and Inventory

Given:

Total flowers in the store: 8100 Initial roses: 70 Initial carnations: 8100 - 70 8030

Understanding the Change in Inventory

The question states that after some roses were sold, the remaining roses made up 40% of the total flowers left. Let's denote:

Remaining roses: R Total remaining flowers: F

Given the condition: R 0.4F

Step-by-Step Solution

Let's analyze the situation step-by-step:

Initial Inventory:

Total flowers: 8100 Roses: 70 Carnations: 8030

Change in Composition:

After some roses are sold, the remaining roses make up 40% of the total flowers left.

Mathematical Representation:

Total remaining flowers, F, will be the sum of the remaining roses and carnations.

Equation Setup:

R 0.4F (where R remaining roses and F total remaining flowers)

Solving for Total Remaining Flowers:

Roses sold 70 - R Total remaining flowers F 8030 R Since R 0.4F, we can substitute F in terms of R:

[ F 2.5R ]

Therefore, we can write:

[ 8030 R 2.5R ]

Solving for R:

[ 8030 1.5R ] [ R frac{8030}{1.5} approx 5353.33 ] Calculation of Remaining Roses:

Remaining roses 70 - R 70 - 5353.33 40 (approx. 4000 when considering whole numbers)

Verification:

Total remaining flowers: 8030 40 8070 %

Final Calculation of Roses Sold

Roses sold 70 - 40 30

Therefore, the number of roses that were sold is 30.

Conclusion

This problem involves a detailed calculation of inventory changes and percentages. It's essential to carefully track the initial and final conditions and apply logical reasoning to reach the solution.

Mathematical Puzzle in Summary

The problem can be summarized as follows:

Total initial flowers: 8100 Initial roses: 70 Initial carnations: 8030 After some roses are sold, the remaining roses are 40% of the total remaining flowers.

The solution involves:

Identifying the remaining roses and total remaining flowers. Solving the equation using the given conditions. Calculating the number of roses sold.

The final answer is that 30 roses were sold.