Sam, Oliver and Harry bought some cupcakes. After Sam ate ³₈ of his cupcakes, Oliver ate ⁴₅ of his cupcakes and Harry ate 3 cupcakes, each of them had the same number of cupcakes left. Sam had 102 less cupcakes than Oliver at first.

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

	Sam	Oliver	Harry
Before	8 u	5x5 = 25 u	5 u + 3
Change	- 3 u	- 4x5 = - 20 u	- 3
After	5 u	1x5 = 5 u	5 u

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

Number of cupcakes that Sam had less than Oliver at first
= 25 u - 8 u
= 17 u

17 u = 102

1 u = 102 ÷ 17 = 6

Number of cupcakes that Sam had at first
= 8 u
= 8 x 6
= 48 

(b)
Total number of cupcakes that the 3 of them bought
= 8 u + 25 u + 5 u + 3
= 38 u + 3
= 38 x 6 + 3
= 228 + 3
= 231

Answer(s): (a) 48; (b) 231