A bookshop sells pens in packs of 5 and 8. At first, there were 3 times as many packs of 5 as packs of 8. After selling half of the packs of 5 and some packs of 8, Mr Chen packs 20 additional packs of 8. How many packs of 5 and 8 are sold if there are 6 times as many packs of 5 as packs of 8 and there is a total of 152 unsold pens?

	Packs of 5	Packs of 8
Comparing the number of packs at first	3x4 = 12 u	1x4 = 4 u
Before	2x6 = 12 u
Change 1	- 1x6 = - 6 u	- ?
Change 2		+ 20
After	1x6 = 6 u
Comparing the number of packs in the end	6 u	1 u

The number of packs of 5 in the end is repeated. Make the number of packs of 5 in the end the same. LCM of 1 and 6 is 6.

The number of packs of 5 at first is repeated. Make the number of packs of 5 at first the same. LCM of 12 and 3 is 12.

Number of pens left unsold	Packs of 5	Packs of 8	Total
Number	6 u	1 u
Value	5	8
Total value	30 u	8 u	38 u

Total number of pens left unsold
= (6 u x 5) + (1 u x 8)
= 30 u + 8 u
= 38 u

38 u = 152

1 u = 152 ÷ 38 = 4

Number of packs of 5 and 8  sold
= 6 u + (4 u - 1 u) + 20
= 6 u + 3 u + 20
= 9 u + 20
= 9 x 4 + 20
= 36 + 20
= 56

Answer(s): 56