A bookshop sells pencils in packs of 3 and 5. At first, there were 4 times as many packs of 3 as packs of 5. After selling half of the packs of 3 and some packs of 5, Mr Lim packs 19 additional packs of 5. How many packs of 3 and 5 are sold if there are 6 times as many packs of 3 as packs of 5 and there is a total of 138 unsold pencils?
| |
Packs of 3 |
Packs of 5 |
Comparing the number
of packs at first |
4x3 =
12 u |
1x3 =
3 u |
| Before |
2x6 =
12 u |
|
| Change 1 |
- 1x6 =
- 6 u |
- ? |
| Change 2 |
|
+ 19 |
| After |
1x6 =
6 u |
|
Comparing the number
of packs in the end |
6 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 6 is 6.
The number of packs of 3 at first is repeated. Make the number of packs of 3 at first the same. LCM of 12 and 4 is 12.
Number of pencils
left unsold |
Packs of 3
|
Packs of 5
|
Total
|
| Number |
6 u |
1 u |
|
| Value |
3 |
5 |
|
| Total value |
18 u |
5 u |
23 u |
Total number of pencils left unsold
= (6 u x 3) + (1 u x 5)
= 18 u + 5 u
= 23 u
23 u = 138
1 u = 138 ÷ 23 = 6
Number of packs of 3 and 5 sold
= 6 u + (3 u - 1 u) + 19
= 6 u + 2 u + 19
= 8 u + 19
= 8 x 6 + 19
= 48 + 19
= 67
Answer(s): 67
