A bookshop sells notebooks in packs of 2 and 3. At first, there were 4 times as many packs of 2 as packs of 3. After selling half of the packs of 2 and some packs of 3, Mr Loh packs 5 additional packs of 3. How many packs of 2 and 3 are sold if there are 6 times as many packs of 2 as packs of 3 and there is a total of 45 unsold notebooks?
| |
Packs of 2 |
Packs of 3 |
Comparing the number
of packs at first |
4x3 =
12 u |
1x3 =
3 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 4 is 12.
Number of notebooks
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 notebooks 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 2 and 3 sold
= 6 u + (3 u - 1 u) + 5
= 6 u + 2 u + 5
= 8 u + 5
= 8 x 3 + 5
= 24 + 5
= 29
Answer(s): 29
