A bookstore sells files in packs of 3 and 4. At first, there were 6 times as many packs of 3 as packs of 4. After selling half of the packs of 3 and some packs of 4, Mr Chye packs 13 additional packs of 4. How many packs of 3 are sold if there are 6 times as many packs of 3 as packs of 4 and there is a total of 132 unsold files?
| |
Packs of 3 |
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 |
|
+ 13 |
| After |
1x6 =
6 u |
|
Comparing the number
of packs in the end |
6 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 6 is 6.
The number of packs of 3 at first is repeated. Make the number of packs of 3 at first the same. LCM of 12 and 6 is 12.
Number of files
left unsold |
Packs of 3
|
Packs of 4
|
Total
|
| Number |
6 u |
1 u |
|
| Value |
3 |
4 |
|
| Total value |
18 u |
4 u |
22 u |
Total number of files left unsold
= (6 u x 3) + (1 u x 4)
= 18 u + 4 u
= 22 u
22 u = 132
1 u = 132 ÷ 22 = 6
Number of packs of 4 sold
= (2 u - 1 u) + 13
= 1 u + 13
= 1 x 6 + 13
= 6 + 13
= 19
Answer(s): 19
