A bookstore sells notebooks in packs of 3 and 6. At first, there were 6 times as many packs of 3 as packs of 6. After selling half of the packs of 3 and some packs of 6, Mr Tang packs 19 additional packs of 6. How many packs of 3 and 6 are sold if there are 6 times as many packs of 3 as packs of 6 and there is a total of 168 unsold notebooks?
| |
Packs of 3 |
Packs of 6 |
Comparing the number
of packs at first |
6x2 =
12 u |
1x2 =
2 u |
| Before |
2x6 =
12 u |
|
| Change 1 |
- 1x6 =
- 6 u |
- ? |
| Change 2 |
|
+ 19 |
| After |
1x6 =
6 u |
|
Comparing the number
of packs in the end |
6 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 6 is 6.
The number of packs of 3 at first is repeated. Make the number of packs of 3 at first the same. LCM of 12 and 6 is 12.
Number of notebooks
left unsold |
Packs of 3
|
Packs of 6
|
Total
|
| Number |
6 u |
1 u |
|
| Value |
3 |
6 |
|
| Total value |
18 u |
6 u |
24 u |
Total number of notebooks left unsold
= (6 u x 3) + (1 u x 6)
= 18 u + 6 u
= 24 u
24 u = 168
1 u = 168 ÷ 24 = 7
Number of packs of 3 and 6 sold
= 6 u + (2 u - 1 u) + 19
= 6 u + 1 u + 19
= 7 u + 19
= 7 x 7 + 19
= 49 + 19
= 68
Answer(s): 68
