A bookstore sells files in packs of 4 and 6. At first, there were 8 times as many packs of 4 as packs of 6. After selling half of the packs of 4 and some packs of 6, Mr Chen packs 20 additional packs of 6. How many packs of 4 and 6 are sold if there are 8 times as many packs of 4 as packs of 6 and there is a total of 190 unsold files?
| |
Packs of 4 |
Packs of 6 |
Comparing the number
of packs at first |
8x2 =
16 u |
1x2 =
2 u |
| Before |
2x8 =
16 u |
|
| Change 1 |
- 1x8 =
- 8 u |
- ? |
| Change 2 |
|
+ 20 |
| After |
1x8 =
8 u |
|
Comparing the number
of packs in the end |
8 u |
1 u |
The number of packs of 4 in the end is repeated. Make the number of packs of 4 in the end the same. LCM of 1 and 8 is 8.
The number of packs of 4 at first is repeated. Make the number of packs of 4 at first the same. LCM of 16 and 8 is 16.
Number of files
left unsold |
Packs of 4
|
Packs of 6
|
Total
|
| Number |
8 u |
1 u |
|
| Value |
4 |
6 |
|
| Total value |
32 u |
6 u |
38 u |
Total number of files left unsold
= (8 u x 4) + (1 u x 6)
= 32 u + 6 u
= 38 u
38 u = 190
1 u = 190 ÷ 38 = 5
Number of packs of 4 and 6 sold
= 8 u + (2 u - 1 u) + 20
= 8 u + 1 u + 20
= 9 u + 20
= 9 x 5 + 20
= 45 + 20
= 65
Answer(s): 65
