A stationery booth sells files in packs of 4 and 6. At first, there were 8 times as many packs of 4 as packs of 6. After selling half of the packs of 4 and some packs of 6, Mr Yang packs 12 additional packs of 6. How many packs of 4 and 6 are sold if there are 8 times as many packs of 4 as packs of 6 and there is a total of 228 unsold files?

	Packs of 4	Packs of 6
Comparing the number of packs at first	8x2 = 16 u	1x2 = 2 u
Before	2x8 = 16 u
Change 1	- 1x8 = - 8 u	- ?
Change 2		+ 12
After	1x8 = 8 u
Comparing the number of packs in the end	8 u	1 u

The number of packs of 4 in the end is repeated. Make the number of packs of 4 in the end the same. LCM of 1 and 8 is 8.

The number of packs of 4 at first is repeated. Make the number of packs of 4 at first the same. LCM of 16 and 8 is 16.

Number of files left unsold	Packs of 4	Packs of 6	Total
Number	8 u	1 u
Value	4	6
Total value	32 u	6 u	38 u

Total number of files left unsold
= (8 u x 4) + (1 u x 6)
= 32 u + 6 u
= 38 u

38 u = 228

1 u = 228 ÷ 38 = 6

Number of packs of 4 and 6  sold
= 8 u + (2 u - 1 u) + 12
= 8 u + 1 u + 12
= 9 u + 12
= 9 x 6 + 12
= 54 + 12
= 66

Answer(s): 66