A stationery kiosk sells pencils in packs of 2 and 5. At first, there were 4 times as many packs of 2 as packs of 5. After selling half of the packs of 2 and some packs of 5, Mr Ong packs 10 additional packs of 5. How many packs of 2 are sold if there are 8 times as many packs of 2 as packs of 5 and there is a total of 105 unsold pencils?
| |
Packs of 2 |
Packs of 5 |
Comparing the number
of packs at first |
4x4 =
16 u |
1x4 =
4 u |
| Before |
2x8 =
16 u |
|
| Change 1 |
- 1x8 =
- 8 u |
- ? |
| Change 2 |
|
+ 10 |
| 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 4 is 16.
Number of pencils
left unsold |
Packs of 2
|
Packs of 5
|
Total
|
| Number |
8 u |
1 u |
|
| Value |
2 |
5 |
|
| Total value |
16 u |
5 u |
21 u |
Total number of pencils left unsold
= (8 u x 2) + (1 u x 5)
= 16 u + 5 u
= 21 u
21 u = 105
1 u = 105 ÷ 21 = 5
Number of packs of 5 sold
= (4 u - 1 u) + 10
= 3 u + 10
= 3 x 5 + 10
= 15 + 10
= 25
Answer(s): 25
