The answer is 22
The sum of two numbers is 48:
x + y = 48 ⇒ x = 48 - y
One third of one number is 5 greater than one sixth of another number:
1/3x =5 + 1/6 y
1/3(48 - y) = 5 + 1/6y
1/3 48 - 1/3 y = 5 + 1/6 y
16 - 1/3y = 5 + 1/6y
16 - 5 = 1/6y + 1/3y
11 = 1/6y + 2/6y
11 = 3/6y
y = 11 * 6 / 3
y = 22
x = 48 - y
x = 48 - 22
x = 26
The smallest number is 22.
