Howard and Daniel had 40 puffs altogether. After Howard ate ¹₅ of his puffs and Daniel ate 6 puffs, the number of puffs Daniel had left was thrice the number of puffs Howard had left. How many more puffs did Daniel have than Howard at first?

	Howard	Daniel	Total
Before	5 u	12 u + 6	40
Change	- 1 u	- 6
After	4 u
Comparing Howard and Daniel in the end	1x4 = 4 u	3x4 = 12 u

The number of puffs that Howard had in the end is the same. Make the number of puffs that Howard had in the end the same.  LCM of 4 and 1 is 4.

Total number of puffs at first
= 5 u + 12 u + 6
= 17 u + 6

17 u + 6 = 40
17 u = 40 - 6
17 u = 34 

1 u = 34 ÷ 17 = 2

Number of puffs that Howard had at first
= 5 u
= 5 x 2
= 10

Number of puffs that Daniel had at first
= 40 - 10
= 30

Number of puffs that Daniel had more than Howard at first
= 30 - 10
= 20

Answer(s): 20