A bookstore sells files in packs of 5 and 8. At first, there were 4 times as many packs of 5 as packs of 8. After selling half of the packs of 5 and some packs of 8, Mr Loo packs 6 additional packs of 8. How many packs of 5 and 8 are sold if there are 6 times as many packs of 5 as packs of 8 and there is a total of 266 unsold files?
| |
Packs of 5 |
Packs of 8 |
Comparing the number
of packs at first |
4x3 =
12 u |
1x3 =
3 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 5 in the end is repeated. Make the number of packs of 5 in the end the same. LCM of 1 and 6 is 6.
The number of packs of 5 at first is repeated. Make the number of packs of 5 at first the same. LCM of 12 and 4 is 12.
Number of files
left unsold |
Packs of 5
|
Packs of 8
|
Total
|
| Number |
6 u |
1 u |
|
| Value |
5 |
8 |
|
| Total value |
30 u |
8 u |
38 u |
Total number of files left unsold
= (6 u x 5) + (1 u x 8)
= 30 u + 8 u
= 38 u
38 u = 266
1 u = 266 ÷ 38 = 7
Number of packs of 5 and 8 sold
= 6 u + (3 u - 1 u) + 6
= 6 u + 2 u + 6
= 8 u + 6
= 8 x 7 + 6
= 56 + 6
= 62
Answer(s): 62
