A bookshop sells files in packs of 2 and 3. At first, there were 6 times as many packs of 2 as packs of 3. After selling half of the packs of 2 and some packs of 3, Mr Yeo packs 5 additional packs of 3. How many packs of 2 are sold if there are 6 times as many packs of 2 as packs of 3 and there is a total of 45 unsold files?
|
Packs of 2 |
Packs of 3 |
Comparing the number of packs at first |
6x2 = 12 u |
1x2 = 2 u |
Before |
2x6 = 12 u |
|
Change 1 |
- 1x6 = - 6 u |
- ? |
Change 2 |
|
+ 5 |
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 3
|
Total
|
Number |
6 u |
1 u |
|
Value |
2 |
3 |
|
Total value |
12 u |
3 u |
15 u |
Total number of files left unsold
= (6 u x 2) + (1 u x 3)
= 12 u + 3 u
= 15 u
15 u = 45
1 u = 45 ÷ 15 = 3
Number of packs of 3 sold
= (2 u - 1 u) + 5
= 1 u + 5
= 1 x 3 + 5
= 3 + 5
= 8
Answer(s): 8