Who used maximum number of pages in the album if all 3 of them had the SAME NUMBER OF stamps?

Answer

To solve the problem, we need to determine how many pages each person used if they all ended up with the same number of stamps. 1. **Let x be the total number of stamps each person has.** 2. **Calculate the number of pages for each individual:** - **Ramya:** She pastes 4 stamps per page, so the number of pages (P_r) she uses is: P_r = x / 4 - **Rajul:** He pastes 9 stamps per page, so the number of pages (P_j) he uses is: P_j = x / 9 - **Ruby:** She pastes 6 stamps per page, so the number of pages (P_u) she uses is: P_u = x / 6 3. **Express the number of pages in terms of a common multiple of the page capacities:** To find a common number of stamps (x) that results in integer pages for all, we look for the least common multiple (LCM) of the stamps per page. 4. **Find the LCM of the stamp counts (4, 9, and 6):** - Prime factorization: - 4 = 2^2 - 9 = 3^2 - 6 = 2^1 * 3^1 - The LCM would take the highest power of each prime: - LCM = 2^2 * 3^2 = 4 * 9 = 36 5. **Calculate pages for each using x = 36 stamps:** - For Ramya: P_r = 36 / 4 = 9 pages - For Rajul: P_j = 36 / 9 = 4 pages - For Ruby: P_u = 36 / 6 = 6 pages 6. **Conclusion:** - Comparing the pages: Ramya = 9, Rajul = 4, Ruby = 6. - Therefore, Ramya used the maximum number of pages. Final Answer: Ramya used the maximum number of pages.