Neave and Luke had 69 macarons altogether. After Neave ate ¹₄ of his macarons and Luke ate 9 macarons, the number of macarons Luke had left was twice the number of macarons Neave had left. How many more macarons did Luke have than Neave at first?

	Neave	Luke	Total
Before	4 u	6 u + 9	69
Change	- 1 u	- 9
After	3 u
Comparing Neave and Luke in the end	1x3 = 3 u	2x3 = 6 u

The number of macarons that Neave had in the end is the same. Make the number of macarons that Neave had in the end the same.  LCM of 3 and 1 is 3.

Total number of macarons at first
= 4 u + 6 u + 9
= 10 u + 9

10 u + 9 = 69
10 u = 69 - 9
10 u = 60 

1 u = 60 ÷ 10 = 6

Number of macarons that Neave had at first
= 4 u
= 4 x 6
= 24

Number of macarons that Luke had at first
= 69 - 24
= 45

Number of macarons that Luke had more than Neave at first
= 45 - 24
= 21

Answer(s): 21