A stationery kiosk sells notebooks in packs of 4 and 5. At first, there were 6 times as many packs of 4 as packs of 5. After selling half of the packs of 4 and some packs of 5, Mr Long packs 16 additional packs of 5. How many packs of 4 and 5 are sold if there are 6 times as many packs of 4 as packs of 5 and there is a total of 58 unsold notebooks?
| |
Packs of 4 |
Packs of 5 |
Comparing the number
of packs at first |
6x2 =
12 u |
1x2 =
2 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 4 in the end is repeated. Make the number of packs of 4 in the end the same. LCM of 1 and 6 is 6.
The number of packs of 4 at first is repeated. Make the number of packs of 4 at first the same. LCM of 12 and 6 is 12.
Number of notebooks
left unsold |
Packs of 4
|
Packs of 5
|
Total
|
| Number |
6 u |
1 u |
|
| Value |
4 |
5 |
|
| Total value |
24 u |
5 u |
29 u |
Total number of notebooks left unsold
= (6 u x 4) + (1 u x 5)
= 24 u + 5 u
= 29 u
29 u = 58
1 u = 58 ÷ 29 = 2
Number of packs of 4 and 5 sold
= 6 u + (2 u - 1 u) + 16
= 6 u + 1 u + 16
= 7 u + 16
= 7 x 2 + 16
= 14 + 16
= 30
Answer(s): 30
