A bookstore sells markers in packs of 2 and 3. At first, there were 8 times as many packs of 2 as packs of 3. After selling half of the packs of 2 and some packs of 3, Mr Long packs 6 additional packs of 3. How many packs of 2 are sold if there are 8 times as many packs of 2 as packs of 3 and there is a total of 38 unsold markers?
| |
Packs of 2 |
Packs of 3 |
Comparing the number
of packs at first |
8x2 =
16 u |
1x2 =
2 u |
| Before |
2x8 =
16 u |
|
| Change 1 |
- 1x8 =
- 8 u |
- ? |
| Change 2 |
|
+ 6 |
| After |
1x8 =
8 u |
|
Comparing the number
of packs in the end |
8 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 8 is 8.
The number of packs of 2 at first is repeated. Make the number of packs of 2 at first the same. LCM of 16 and 8 is 16.
Number of markers
left unsold |
Packs of 2
|
Packs of 3
|
Total
|
| Number |
8 u |
1 u |
|
| Value |
2 |
3 |
|
| Total value |
16 u |
3 u |
19 u |
Total number of markers left unsold
= (8 u x 2) + (1 u x 3)
= 16 u + 3 u
= 19 u
19 u = 38
1 u = 38 ÷ 19 = 2
Number of packs of 3 sold
= (2 u - 1 u) + 6
= 1 u + 6
= 1 x 2 + 6
= 2 + 6
= 8
Answer(s): 8
