One third of a number is 15 less than five sixths of a the number find the number

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

1/3 times x = 5/6 times x - 15

subtract 5/6 times x from both sides:

-1/2 times x=-15

divide by - 1/2 on both sides

x=30