A stationery kiosk sells files in packs of 3 and 6. At first, there were 10 times as many packs of 3 as packs of 6. After selling half of the packs of 3 and some packs of 6, Mr Chiam packs 9 additional packs of 6. How many packs of 3 and 6 are sold if there are 10 times as many packs of 3 as packs of 6 and there is a total of 180 unsold files?
| |
Packs of 3 |
Packs of 6 |
Comparing the number
of packs at first |
10x2 =
20 u |
1x2 =
2 u |
| Before |
2x10 =
20 u |
|
| Change 1 |
- 1x10 =
- 10 u |
- ? |
| Change 2 |
|
+ 9 |
| After |
1x10 =
10 u |
|
Comparing the number
of packs in the end |
10 u |
1 u |
The number of packs of 3 in the end is repeated. Make the number of packs of 3 in the end the same. LCM of 1 and 10 is 10.
The number of packs of 3 at first is repeated. Make the number of packs of 3 at first the same. LCM of 20 and 10 is 20.
Number of files
left unsold |
Packs of 3
|
Packs of 6
|
Total
|
| Number |
10 u |
1 u |
|
| Value |
3 |
6 |
|
| Total value |
30 u |
6 u |
36 u |
Total number of files left unsold
= (10 u x 3) + (1 u x 6)
= 30 u + 6 u
= 36 u
36 u = 180
1 u = 180 ÷ 36 = 5
Number of packs of 3 and 6 sold
= 10 u + (2 u - 1 u) + 9
= 10 u + 1 u + 9
= 11 u + 9
= 11 x 5 + 9
= 55 + 9
= 64
Answer(s): 64
