Cole and Harry had 69 cupcakes altogether. After Cole ate ¹₆ of his cupcakes and Harry ate 5 cupcakes, the number of cupcakes Harry had left was twice the number of cupcakes Cole had left. How many more cupcakes did Harry have than Cole at first?

	Cole	Harry	Total
Before	6 u	10 u + 5	69
Change	- 1 u	- 5
After	5 u
Comparing Cole and Harry in the end	1x5 = 5 u	2x5 = 10 u

The number of cupcakes that Cole had in the end is the same. Make the number of cupcakes that Cole had in the end the same.  LCM of 5 and 1 is 5.

Total number of cupcakes at first
= 6 u + 10 u + 5
= 16 u + 5

16 u + 5 = 69
16 u = 69 - 5
16 u = 64 

1 u = 64 ÷ 16 = 4

Number of cupcakes that Cole had at first
= 6 u
= 6 x 4
= 24

Number of cupcakes that Harry had at first
= 69 - 24
= 45

Number of cupcakes that Harry had more than Cole at first
= 45 - 24
= 21

Answer(s): 21