Perry and Jack had 43 muffins altogether. After Perry ate ¹₃ of his muffins and Jack ate 7 muffins, the number of muffins Jack had left was thrice the number of muffins Perry had left. How many more muffins did Jack have than Perry at first?

	Perry	Jack	Total
Before	3 u	6 u + 7	43
Change	- 1 u	- 7
After	2 u
Comparing Perry and Jack in the end	1x2 = 2 u	3x2 = 6 u

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

Total number of muffins at first
= 3 u + 6 u + 7
= 9 u + 7

9 u + 7 = 43
9 u = 43 - 7
9 u = 36 

1 u = 36 ÷ 9 = 4

Number of muffins that Perry had at first
= 3 u
= 3 x 4
= 12

Number of muffins that Jack had at first
= 43 - 12
= 31

Number of muffins that Jack had more than Perry at first
= 31 - 12
= 19

Answer(s): 19