A stationery booth sells pencils in packs of 2 and 3. At first, there were 10 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 18 additional packs of 3. How many packs of 2 and 3 are sold if there are 10 times as many packs of 2 as packs of 3 and there is a total of 92 unsold pencils?
| |
Packs of 2 |
Packs of 3 |
Comparing the number
of packs at first |
10x2 =
20 u |
1x2 =
2 u |
| Before |
2x10 =
20 u |
|
| Change 1 |
- 1x10 =
- 10 u |
- ? |
| Change 2 |
|
+ 18 |
| 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 10 is 20.
Number of pencils
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 pencils left unsold
= (10 u x 2) + (1 u x 3)
= 20 u + 3 u
= 23 u
23 u = 92
1 u = 92 ÷ 23 = 4
Number of packs of 2 and 3 sold
= 10 u + (2 u - 1 u) + 18
= 10 u + 1 u + 18
= 11 u + 18
= 11 x 4 + 18
= 44 + 18
= 62
Answer(s): 62
