A stationery booth sells files in packs of 2 and 4. At first, there were 6 times as many packs of 2 as packs of 4. After selling half of the packs of 2 and some packs of 4, Mr Tay packs 18 additional packs of 4. How many packs of 2 and 4 are sold if there are 6 times as many packs of 2 as packs of 4 and there is a total of 112 unsold files?
| |
Packs of 2 |
Packs of 4 |
Comparing the number
of packs at first |
6x2 =
12 u |
1x2 =
2 u |
| Before |
2x6 =
12 u |
|
| Change 1 |
- 1x6 =
- 6 u |
- ? |
| Change 2 |
|
+ 18 |
| After |
1x6 =
6 u |
|
Comparing the number
of packs in the end |
6 u |
1 u |
The number of packs of 2 in the end is repeated. Make the number of packs of 2 in the end the same. LCM of 1 and 6 is 6.
The number of packs of 2 at first is repeated. Make the number of packs of 2 at first the same. LCM of 12 and 6 is 12.
Number of files
left unsold |
Packs of 2
|
Packs of 4
|
Total
|
| Number |
6 u |
1 u |
|
| Value |
2 |
4 |
|
| Total value |
12 u |
4 u |
16 u |
Total number of files left unsold
= (6 u x 2) + (1 u x 4)
= 12 u + 4 u
= 16 u
16 u = 112
1 u = 112 ÷ 16 = 7
Number of packs of 2 and 4 sold
= 6 u + (2 u - 1 u) + 18
= 6 u + 1 u + 18
= 7 u + 18
= 7 x 7 + 18
= 49 + 18
= 67
Answer(s): 67
