Calculation of Unpainted House Area: A Mathematical Puzzle Solved

Puzzles and riddles are fun but can also be quite challenging, especially when they involve a mix of fractions and common denominators. In this article, we will explore a real-life scenario involving house painting and break down the calculations step by step. This problem not only tests mathematical skills but also emphasizes the importance of precision and accuracy in real-world situations.

Context and Problem Statement

Three individuals, Paolo, Russell, and Jojo, agreed to paint a house together. Paolo did 1/8 of the job, Russell did 2/5 of the job, and Jojo did 1/3 of the work. The question is, what fraction of the house is still left unpainted? Let's walk through the solution process to find the exact fraction of the work that remains to be completed.

Step-by-Step Solution

Identifying Common Denominators

The first step is to identify the least common multiple (LCM) of the denominators 8, 5, and 3. The LCM of these numbers is 120.

Calculation of Painted Areas

Let us assume the total area of the house is 120 units for simplicity. We can now calculate the areas painted by each individual based on their work share:

Paolo painted 15 units (120 units * 1/8). Russell painted 48 units (120 units * 2/5). Jojo painted 40 units (120 units * 1/3).

The total area painted by Paolo, Russell, and Jojo together is 103 units (15 48 40).

Remaining Area Calculation

To find out how much of the house is still left to be painted, we subtract the total painted area from the entire house area:

120 units - 103 units 17 units.

Expressing this as a fraction of the entire house, we get:

17/120.

Verification of Other Answers

Other solutions to this problem have been shared, including:

41/120 (which can be reduced to 17/120) The total area painted can be calculated as follows: 1 - (1/8) - (2/5) - (1/3) 1 - 15/120 - 48/120 - 40/120 17/120

These solutions corroborate that the remaining unpainted fraction of the house is indeed 17/120. This method of solving the problem shows that even with different approaches, the final answer is consistent.

Conclusion

This exercise not only helps in solving a practical problem related to house painting but also demonstrates the importance of common denominators and fraction arithmetic in everyday calculations. Whether you're a homeowner, a mathematician, or someone interested in problem-solving, understanding these concepts can be invaluable.

By breaking down the problem into smaller, manageable steps and using a consistent approach, we can accurately determine the remaining unpainted area of the house. This method can be applied to similar real-world scenarios, enhancing our problem-solving skills and ensuring precision in our calculations.