A bookshop sells notebooks in packs of 3 and 4. At first, there were 5 times as many packs of 3 as packs of 4. After selling half of the packs of 3 and some packs of 4, Mr Lin packs 18 additional packs of 4. How many packs of 3 are sold if there are 10 times as many packs of 3 as packs of 4 and there is a total of 306 unsold notebooks?
| |
Packs of 3 |
Packs of 4 |
Comparing the number
of packs at first |
5x4 =
20 u |
1x4 =
4 u |
| Before |
2x10 =
20 u |
|
| Change 1 |
- 1x10 =
- 10 u |
- ? |
| Change 2 |
|
+ 18 |
| After |
1x10 =
10 u |
|
Comparing the number
of packs in the end |
10 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 10 is 10.
The number of packs of 3 at first is repeated. Make the number of packs of 3 at first the same. LCM of 20 and 5 is 20.
Number of notebooks
left unsold |
Packs of 3
|
Packs of 4
|
Total
|
| Number |
10 u |
1 u |
|
| Value |
3 |
4 |
|
| Total value |
30 u |
4 u |
34 u |
Total number of notebooks left unsold
= (10 u x 3) + (1 u x 4)
= 30 u + 4 u
= 34 u
34 u = 306
1 u = 306 ÷ 34 = 9
Number of packs of 4 sold
= (4 u - 1 u) + 18
= 3 u + 18
= 3 x 9 + 18
= 27 + 18
= 45
Answer(s): 45
