A bookshop sells pencils in packs of 4 and 7. At first, there were 10 times as many packs of 4 as packs of 7. After selling half of the packs of 4 and some packs of 7, Mr Sim packs 18 additional packs of 7. How many packs of 4 and 7 are sold if there are 10 times as many packs of 4 as packs of 7 and there is a total of 141 unsold pencils?

	Packs of 4	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		+ 18
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 pencils left unsold	Packs of 4	Packs of 7	Total
Number	10 u	1 u
Value	4	7
Total value	40 u	7 u	47 u

Total number of pencils left unsold
= (10 u x 4) + (1 u x 7)
= 40 u + 7 u
= 47 u

47 u = 141

1 u = 141 ÷ 47 = 3

Number of packs of 4 and 7  sold
= 10 u + (2 u - 1 u) + 18
= 10 u + 1 u + 18
= 11 u + 18
= 11 x 3 + 18
= 33 + 18
= 51

Answer(s): 51