A bookshop sells markers in packs of 4 and 7. At first, there were 4 times as many packs of 4 as packs of 7. After selling half of the packs of 4 and some packs of 7, Mr Peh packs 11 additional packs of 7. How many packs of 4 and 7 are sold if there are 6 times as many packs of 4 as packs of 7 and there is a total of 279 unsold markers?

	Packs of 4	Packs of 7
Comparing the number of packs at first	4x3 = 12 u	1x3 = 3 u
Before	2x6 = 12 u
Change 1	- 1x6 = - 6 u	- ?
Change 2		+ 11
After	1x6 = 6 u
Comparing the number of packs in the end	6 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 6 is 6.

The number of packs of 4 at first is repeated. Make the number of packs of 4 at first the same. LCM of 12 and 4 is 12.

Number of markers left unsold	Packs of 4	Packs of 7	Total
Number	6 u	1 u
Value	4	7
Total value	24 u	7 u	31 u

Total number of markers left unsold
= (6 u x 4) + (1 u x 7)
= 24 u + 7 u
= 31 u

31 u = 279

1 u = 279 ÷ 31 = 9

Number of packs of 4 and 7  sold
= 6 u + (3 u - 1 u) + 11
= 6 u + 2 u + 11
= 8 u + 11
= 8 x 9 + 11
= 72 + 11
= 83

Answer(s): 83