A group of engineers, accountants, and architects has a combined age of 2750 years, with an average age of 50 years. Their average age would have climbed by 7 years if the age of each engineer had increased by 3 years, of each accountant by 8 years, and of each architect by 10 years. Find the minimum possible number of accountants in the group.

Let E, A, R be the number of engineers, accountants, and architects. Total people N = 2750/50 = 55. New average = 57. Total age increase = 55 * 7 = 385. 3E + 8A + 10R = 385. E + A + R = 55. Substitute E = 55 - A - R: 3(55-A-R) + 8A + 10R = 385. 165 - 3A - 3R + 8A + 10R = 385. 5A + 7R = 220. For minimum A, R must be maximum. Since A+R < 55, try R=30, 5A=10, A=2. If R=30, A=2, E=23. This works.