A stationery kiosk sells pencils in packs of 3 and 5. At first, there were 10 times as many packs of 3 as packs of 5. After selling half of the packs of 3 and some packs of 5, Mr Ang packs 8 additional packs of 5. How many packs of 3 are sold if there are 10 times as many packs of 3 as packs of 5 and there is a total of 70 unsold pencils?
| |
Packs of 3 |
Packs of 5 |
Comparing the number
of packs at first |
10x2 =
20 u |
1x2 =
2 u |
| Before |
2x10 =
20 u |
|
| Change 1 |
- 1x10 =
- 10 u |
- ? |
| Change 2 |
|
+ 8 |
| 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 10 is 20.
Number of pencils
left unsold |
Packs of 3
|
Packs of 5
|
Total
|
| Number |
10 u |
1 u |
|
| Value |
3 |
5 |
|
| Total value |
30 u |
5 u |
35 u |
Total number of pencils left unsold
= (10 u x 3) + (1 u x 5)
= 30 u + 5 u
= 35 u
35 u = 70
1 u = 70 ÷ 35 = 2
Number of packs of 5 sold
= (2 u - 1 u) + 8
= 1 u + 8
= 1 x 2 + 8
= 2 + 8
= 10
Answer(s): 10
