A bookshop sells pencils in packs of 5 and 7. At first, there were 10 times as many packs of 5 as packs of 7. After selling half of the packs of 5 and some packs of 7, Mr Yee packs 14 additional packs of 7. How many packs of 5 and 7 are sold if there are 10 times as many packs of 5 as packs of 7 and there is a total of 285 unsold pencils?

	Packs of 5	Packs of 7
Comparing the number of packs at first	10x2 = 20 u	1x2 = 2 u
Before	2x10 = 20 u
Change 1	- 1x10 = - 10 u	- ?
Change 2		+ 14
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 10 is 20.

Number of pencils left unsold	Packs of 5	Packs of 7	Total
Number	10 u	1 u
Value	5	7
Total value	50 u	7 u	57 u

Total number of pencils left unsold
= (10 u x 5) + (1 u x 7)
= 50 u + 7 u
= 57 u

57 u = 285

1 u = 285 ÷ 57 = 5

Number of packs of 5 and 7  sold
= 10 u + (2 u - 1 u) + 14
= 10 u + 1 u + 14
= 11 u + 14
= 11 x 5 + 14
= 55 + 14
= 69

Answer(s): 69