A bookstore sells pencils in packs of 2 and 5. At first, there were 3 times as many packs of 2 as packs of 5. After selling half of the packs of 2 and some packs of 5, Mr Chew packs 5 additional packs of 5. How many packs of 2 are sold if there are 6 times as many packs of 2 as packs of 5 and there is a total of 51 unsold pencils?
| |
Packs of 2 |
Packs of 5 |
Comparing the number
of packs at first |
3x4 =
12 u |
1x4 =
4 u |
| Before |
2x6 =
12 u |
|
| Change 1 |
- 1x6 =
- 6 u |
- ? |
| Change 2 |
|
+ 5 |
| After |
1x6 =
6 u |
|
Comparing the number
of packs in the end |
6 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 6 is 6.
The number of packs of 2 at first is repeated. Make the number of packs of 2 at first the same. LCM of 12 and 3 is 12.
Number of pencils
left unsold |
Packs of 2
|
Packs of 5
|
Total
|
| Number |
6 u |
1 u |
|
| Value |
2 |
5 |
|
| Total value |
12 u |
5 u |
17 u |
Total number of pencils left unsold
= (6 u x 2) + (1 u x 5)
= 12 u + 5 u
= 17 u
17 u = 51
1 u = 51 ÷ 17 = 3
Number of packs of 5 sold
= (4 u - 1 u) + 5
= 3 u + 5
= 3 x 3 + 5
= 9 + 5
= 14
Answer(s): 14
