A bookstore sells pens in packs of 2 and 4. At first, there were 8 times as many packs of 2 as packs of 4. After selling half of the packs of 2 and some packs of 4, Mr Chua packs 12 additional packs of 4. How many packs of 2 are sold if there are 8 times as many packs of 2 as packs of 4 and there is a total of 40 unsold pens?
| |
Packs of 2 |
Packs of 4 |
Comparing the number
of packs at first |
8x2 =
16 u |
1x2 =
2 u |
| Before |
2x8 =
16 u |
|
| Change 1 |
- 1x8 =
- 8 u |
- ? |
| Change 2 |
|
+ 12 |
| After |
1x8 =
8 u |
|
Comparing the number
of packs in the end |
8 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 8 is 8.
The number of packs of 2 at first is repeated. Make the number of packs of 2 at first the same. LCM of 16 and 8 is 16.
Number of pens
left unsold |
Packs of 2
|
Packs of 4
|
Total
|
| Number |
8 u |
1 u |
|
| Value |
2 |
4 |
|
| Total value |
16 u |
4 u |
20 u |
Total number of pens left unsold
= (8 u x 2) + (1 u x 4)
= 16 u + 4 u
= 20 u
20 u = 40
1 u = 40 ÷ 20 = 2
Number of packs of 4 sold
= (2 u - 1 u) + 12
= 1 u + 12
= 1 x 2 + 12
= 2 + 12
= 14
Answer(s): 14
