Japheth, Vincent and Valen bought some cupcakes. After Japheth ate ²₅ of his cupcakes, Vincent ate ¹₂ of his cupcakes and Valen ate 3 cupcakes, each of them had the same number of cupcakes left. Japheth had 9 less cupcakes than Vincent at first.

1. How many cupcakes did Japheth have at first?
2. How many cupcakes did the 3 of them buy altogether? 

	Japheth	Vincent	Valen
Before	5 u	2x3 = 6 u	3 u + 3
Change	- 2 u	- 1x3 = - 3 u	- 3
After	3 u	1x3 = 3 u	3 u

(a)
The number of cupcakes that Japheth and Vincent each had in the end is the same. Make the number of cupcakes that Japheth and Vincent each had in the end the same.  LCM of 3 and 1 is 3.

Number of cupcakes that Japheth had less than Vincent at first
= 6 u - 5 u
= 1 u

1 u = 9

1 u = 9 ÷ 1 = 9

Number of cupcakes that Japheth had at first
= 5 u
= 5 x 9
= 45 

(b)
Total number of cupcakes that the 3 of them bought
= 5 u + 6 u + 3 u + 3
= 14 u + 3
= 14 x 9 + 3
= 126 + 3
= 129

Answer(s): (a) 45; (b) 129