Vincent and Jeremy had 45 cupcakes altogether. After Vincent ate ¹₃ of his cupcakes and Jeremy ate 3 cupcakes, the number of cupcakes Jeremy had left was twice the number of cupcakes Vincent had left. How many more cupcakes did Jeremy have than Vincent at first?

	Vincent	Jeremy	Total
Before	3 u	4 u + 3	45
Change	- 1 u	- 3
After	2 u
Comparing Vincent and Jeremy in the end	1x2 = 2 u	2x2 = 4 u

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

Total number of cupcakes at first
= 3 u + 4 u + 3
= 7 u + 3

7 u + 3 = 45
7 u = 45 - 3
7 u = 42 

1 u = 42 ÷ 7 = 6

Number of cupcakes that Vincent had at first
= 3 u
= 3 x 6
= 18

Number of cupcakes that Jeremy had at first
= 45 - 18
= 27

Number of cupcakes that Jeremy had more than Vincent at first
= 27 - 18
= 9

Answer(s): 9