A bookstore sells files in packs of 2 and 3. At first, there were 5 times as many packs of 2 as packs of 3. After selling half of the packs of 2 and some packs of 3, Mr Ma packs 10 additional packs of 3. How many packs of 2 and 3 are sold if there are 10 times as many packs of 2 as packs of 3 and there is a total of 69 unsold files?

	Packs of 2	Packs of 3
Comparing the number of packs at first	5x4 = 20 u	1x4 = 4 u
Before	2x10 = 20 u
Change 1	- 1x10 = - 10 u	- ?
Change 2		+ 10
After	1x10 = 10 u
Comparing the number of packs in the end	10 u	1 u

The number of packs of 2 in the end is repeated. Make the number of packs of 2 in the end the same. LCM of 1 and 10 is 10.

The number of packs of 2 at first is repeated. Make the number of packs of 2 at first the same. LCM of 20 and 5 is 20.

Number of files left unsold	Packs of 2	Packs of 3	Total
Number	10 u	1 u
Value	2	3
Total value	20 u	3 u	23 u

Total number of files left unsold
= (10 u x 2) + (1 u x 3)
= 20 u + 3 u
= 23 u

23 u = 69

1 u = 69 ÷ 23 = 3

Number of packs of 2 and 3  sold
= 10 u + (4 u - 1 u) + 10
= 10 u + 3 u + 10
= 13 u + 10
= 13 x 3 + 10
= 39 + 10
= 49

Answer(s): 49