A stationery kiosk sells pencils in packs of 5 and 8. At first, there were 5 times as many packs of 5 as packs of 8. After selling half of the packs of 5 and some packs of 8, Mr Yong packs 15 additional packs of 8. How many packs of 5 and 8 are sold if there are 10 times as many packs of 5 as packs of 8 and there is a total of 406 unsold pencils?

	Packs of 5	Packs of 8
Comparing the number of packs at first	5x4 = 20 u	1x4 = 4 u
Before	2x10 = 20 u
Change 1	- 1x10 = - 10 u	- ?
Change 2		+ 15
After	1x10 = 10 u
Comparing the number of packs in the end	10 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 10 is 10.

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

Number of pencils left unsold	Packs of 5	Packs of 8	Total
Number	10 u	1 u
Value	5	8
Total value	50 u	8 u	58 u

Total number of pencils left unsold
= (10 u x 5) + (1 u x 8)
= 50 u + 8 u
= 58 u

58 u = 406

1 u = 406 ÷ 58 = 7

Number of packs of 5 and 8  sold
= 10 u + (4 u - 1 u) + 15
= 10 u + 3 u + 15
= 13 u + 15
= 13 x 7 + 15
= 91 + 15
= 106

Answer(s): 106