A stationery booth sells pens in packs of 4 and 5. At first, there were 10 times as many packs of 4 as packs of 5. After selling half of the packs of 4 and some packs of 5, Mr Ang packs 19 additional packs of 5. How many packs of 4 and 5 are sold if there are 10 times as many packs of 4 as packs of 5 and there is a total of 135 unsold pens?

	Packs of 4	Packs of 5
Comparing the number of packs at first	10x2 = 20 u	1x2 = 2 u
Before	2x10 = 20 u
Change 1	- 1x10 = - 10 u	- ?
Change 2		+ 19
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 10 is 20.

Number of pens left unsold	Packs of 4	Packs of 5	Total
Number	10 u	1 u
Value	4	5
Total value	40 u	5 u	45 u

Total number of pens left unsold
= (10 u x 4) + (1 u x 5)
= 40 u + 5 u
= 45 u

45 u = 135

1 u = 135 ÷ 45 = 3

Number of packs of 4 and 5  sold
= 10 u + (2 u - 1 u) + 19
= 10 u + 1 u + 19
= 11 u + 19
= 11 x 3 + 19
= 33 + 19
= 52

Answer(s): 52