The average age of 35 students in a group is 15 years. When the teacher's age is included, the average age of the group increases by 1.25 years. What is the teacher's age (in years)?

The average of 100 numbers is 40. If one of the numbers, 30, is replaced by 70 while keeping the other numbers same, what is the new average?

The arithmetic mean of 22.5, 56, 42.5, 2x + 1, x - 2, 3x, and 36 is 30. Find the value of x (where x > 0).