Question

a number, half of that number, and one-third of that number are added. The result is 22. What is the original number

Answer 1

A number, half of that number, and one-third of that number are added.
This statement can be expressed as:
x + (1/2)x + (1/3)x

The total is 22
x + (1/2)x + (1/3)x = 22

So let's look for x
x + (1/2)x + (1/3)x = 22
(6x + 3x + 2x) / 6 = 22
11x = 132
x = 12

So the original number is 12.