we'll call the number x
one third of the number: 1/3x
fifteen less than five sixths of the number: 5/6x - 15
1/3x = 5/6x - 15
multiply both sides by three
x = 5/2x - 45
multiply both sides by 2
2x = 5x - 90
subtract 5x from both sides
-3x = -90
divide both sides by -3
x = 30