A bookstore sells files in packs of 2 and 4. At first, there were 5 times as many packs of 2 as packs of 4. After selling half of the packs of 2 and some packs of 4, Mr Neo packs 18 additional packs of 4. How many packs of 2 are sold if there are 10 times as many packs of 2 as packs of 4 and there is a total of 216 unsold files?
|
Packs of 2 |
Packs of 4 |
Comparing the number of packs at first |
5x4 = 20 u |
1x4 = 4 u |
Before |
2x10 = 20 u |
|
Change 1 |
- 1x10 = - 10 u |
- ? |
Change 2 |
|
+ 18 |
After |
1x10 = 10 u |
|
Comparing the number of packs in the end |
10 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 10 is 10.
The number of packs of 2 at first is repeated. Make the number of packs of 2 at first the same. LCM of 20 and 5 is 20.
Number of files left unsold |
Packs of 2
|
Packs of 4
|
Total
|
Number |
10 u |
1 u |
|
Value |
2 |
4 |
|
Total value |
20 u |
4 u |
24 u |
Total number of files left unsold
= (10 u x 2) + (1 u x 4)
= 20 u + 4 u
= 24 u
24 u = 216
1 u = 216 ÷ 24 = 9
Number of packs of 4 sold
= (4 u - 1 u) + 18
= 3 u + 18
= 3 x 9 + 18
= 27 + 18
= 45
Answer(s): 45