A stationery kiosk sells staplers in packs of 2 and 3. At first, there were 5 times as many packs of 2 as packs of 3. After selling half of the packs of 2 and some packs of 3, Mr Sih packs 13 additional packs of 3. How many packs of 2 are sold if there are 10 times as many packs of 2 as packs of 3 and there is a total of 161 unsold staplers?
| |
Packs of 2 |
Packs of 3 |
Comparing the number
of packs at first |
5x4 =
20 u |
1x4 =
4 u |
| Before |
2x10 =
20 u |
|
| Change 1 |
- 1x10 =
- 10 u |
- ? |
| Change 2 |
|
+ 13 |
| After |
1x10 =
10 u |
|
Comparing the number
of packs in the end |
10 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 10 is 10.
The number of packs of 2 at first is repeated. Make the number of packs of 2 at first the same. LCM of 20 and 5 is 20.
Number of staplers
left unsold |
Packs of 2
|
Packs of 3
|
Total
|
| Number |
10 u |
1 u |
|
| Value |
2 |
3 |
|
| Total value |
20 u |
3 u |
23 u |
Total number of staplers left unsold
= (10 u x 2) + (1 u x 3)
= 20 u + 3 u
= 23 u
23 u = 161
1 u = 161 ÷ 23 = 7
Number of packs of 3 sold
= (4 u - 1 u) + 13
= 3 u + 13
= 3 x 7 + 13
= 21 + 13
= 34
Answer(s): 34
