A stationery booth sells pencils in packs of 5 and 6. At first, there were 6 times as many packs of 5 as packs of 6. After selling half of the packs of 5 and some packs of 6, Mr Kok packs 10 additional packs of 6. How many packs of 5 and 6 are sold if there are 6 times as many packs of 5 as packs of 6 and there is a total of 108 unsold pencils?
| |
Packs of 5 |
Packs of 6 |
Comparing the number
of packs at first |
6x2 =
12 u |
1x2 =
2 u |
| Before |
2x6 =
12 u |
|
| Change 1 |
- 1x6 =
- 6 u |
- ? |
| Change 2 |
|
+ 10 |
| After |
1x6 =
6 u |
|
Comparing the number
of packs in the end |
6 u |
1 u |
The number of packs of 5 in the end is repeated. Make the number of packs of 5 in the end the same. LCM of 1 and 6 is 6.
The number of packs of 5 at first is repeated. Make the number of packs of 5 at first the same. LCM of 12 and 6 is 12.
Number of pencils
left unsold |
Packs of 5
|
Packs of 6
|
Total
|
| Number |
6 u |
1 u |
|
| Value |
5 |
6 |
|
| Total value |
30 u |
6 u |
36 u |
Total number of pencils left unsold
= (6 u x 5) + (1 u x 6)
= 30 u + 6 u
= 36 u
36 u = 108
1 u = 108 ÷ 36 = 3
Number of packs of 5 and 6 sold
= 6 u + (2 u - 1 u) + 10
= 6 u + 1 u + 10
= 7 u + 10
= 7 x 3 + 10
= 21 + 10
= 31
Answer(s): 31
