A bookshop sells pens in packs of 4 and 6. At first, there were 5 times as many packs of 4 as packs of 6. After selling half of the packs of 4 and some packs of 6, Mr Chan packs 12 additional packs of 6. How many packs of 4 and 6 are sold if there are 10 times as many packs of 4 as packs of 6 and there is a total of 92 unsold pens?

	Packs of 4	Packs of 6
Comparing the number of packs at first	5x4 = 20 u	1x4 = 4 u
Before	2x10 = 20 u
Change 1	- 1x10 = - 10 u	- ?
Change 2		+ 12
After	1x10 = 10 u
Comparing the number of packs in the end	10 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 10 is 10.

The number of packs of 4 at first is repeated. Make the number of packs of 4 at first the same. LCM of 20 and 5 is 20.

Number of pens left unsold	Packs of 4	Packs of 6	Total
Number	10 u	1 u
Value	4	6
Total value	40 u	6 u	46 u

Total number of pens left unsold
= (10 u x 4) + (1 u x 6)
= 40 u + 6 u
= 46 u

46 u = 92

1 u = 92 ÷ 46 = 2

Number of packs of 4 and 6  sold
= 10 u + (4 u - 1 u) + 12
= 10 u + 3 u + 12
= 13 u + 12
= 13 x 2 + 12
= 26 + 12
= 38

Answer(s): 38