Ian and Harry had 83 croissants altogether. After Ian ate ¹₃ of his croissants and Harry ate 6 croissants, the number of croissants Harry had left was four times the number of croissants Ian had left. How many more croissants did Harry have than Ian at first?

	Ian	Harry	Total
Before	3 u	8 u + 6	83
Change	- 1 u	- 6
After	2 u
Comparing Ian and Harry in the end	1x2 = 2 u	4x2 = 8 u

The number of croissants that Ian had in the end is the same. Make the number of croissants that Ian had in the end the same.  LCM of 2 and 1 is 2.

Total number of croissants at first
= 3 u + 8 u + 6
= 11 u + 6

11 u + 6 = 83
11 u = 83 - 6
11 u = 77 

1 u = 77 ÷ 11 = 7

Number of croissants that Ian had at first
= 3 u
= 3 x 7
= 21

Number of croissants that Harry had at first
= 83 - 21
= 62

Number of croissants that Harry had more than Ian at first
= 62 - 21
= 41

Answer(s): 41