Andy, Valen and Paul bought some cupcakes. After Andy ate ²₇ of his cupcakes, Valen ate ¹₂ of his cupcakes and Paul ate 12 cupcakes, each of them had the same number of cupcakes left. Andy had 30 less cupcakes than Valen at first.

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

	Andy	Valen	Paul
Before	7 u	2x5 = 10 u	5 u + 12
Change	- 2 u	- 1x5 = - 5 u	- 12
After	5 u	1x5 = 5 u	5 u

(a)
The number of cupcakes that Andy and Valen each had in the end is the same. Make the number of cupcakes that Andy and Valen each had in the end the same.  LCM of 5 and 1 is 5.

Number of cupcakes that Andy had less than Valen at first
= 10 u - 7 u
= 3 u

3 u = 30

1 u = 30 ÷ 3 = 10

Number of cupcakes that Andy had at first
= 7 u
= 7 x 10
= 70 

(b)
Total number of cupcakes that the 3 of them bought
= 7 u + 10 u + 5 u + 12
= 22 u + 12
= 22 x 10 + 12
= 220 + 12
= 232

Answer(s): (a) 70; (b) 232