A stationery booth sells files in packs of 4 and 7. At first, there were 3 times as many packs of 4 as packs of 7. After selling half of the packs of 4 and some packs of 7, Mr Heng packs 6 additional packs of 7. How many packs of 4 are sold if there are 6 times as many packs of 4 as packs of 7 and there is a total of 310 unsold files?
|
Packs of 4 |
Packs of 7 |
Comparing the number of packs at first |
3x4 = 12 u |
1x4 = 4 u |
Before |
2x6 = 12 u |
|
Change 1 |
- 1x6 = - 6 u |
- ? |
Change 2 |
|
+ 6 |
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 3 is 12.
Number of files 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 files left unsold
= (6 u x 4) + (1 u x 7)
= 24 u + 7 u
= 31 u
31 u = 310
1 u = 310 ÷ 31 = 10
Number of packs of 7 sold
= (4 u - 1 u) + 6
= 3 u + 6
= 3 x 10 + 6
= 30 + 6
= 36
Answer(s): 36