A bookshop sells files in packs of 5 and 7. At first, there were 3 times as many packs of 5 as packs of 7. After selling half of the packs of 5 and some packs of 7, Mr Quek packs 16 additional packs of 7. How many packs of 5 and 7 are sold if there are 6 times as many packs of 5 as packs of 7 and there is a total of 185 unsold files?
| |
Packs of 5 |
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 |
|
+ 16 |
| 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 3 is 12.
Number of files
left unsold |
Packs of 5
|
Packs of 7
|
Total
|
| Number |
6 u |
1 u |
|
| Value |
5 |
7 |
|
| Total value |
30 u |
7 u |
37 u |
Total number of files left unsold
= (6 u x 5) + (1 u x 7)
= 30 u + 7 u
= 37 u
37 u = 185
1 u = 185 ÷ 37 = 5
Number of packs of 5 and 7 sold
= 6 u + (4 u - 1 u) + 16
= 6 u + 3 u + 16
= 9 u + 16
= 9 x 5 + 16
= 45 + 16
= 61
Answer(s): 61
