A bookstore sells pencils in packs of 3 and 4. At first, there were 10 times as many packs of 3 as packs of 4. After selling half of the packs of 3 and some packs of 4, Mr Long packs 18 additional packs of 4. How many packs of 3 are sold if there are 10 times as many packs of 3 as packs of 4 and there is a total of 204 unsold pencils?
|
Packs of 3 |
Packs of 4 |
Comparing the number of packs at first |
10x2 = 20 u |
1x2 = 2 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 3 in the end is repeated. Make the number of packs of 3 in the end the same. LCM of 1 and 10 is 10.
The number of packs of 3 at first is repeated. Make the number of packs of 3 at first the same. LCM of 20 and 10 is 20.
Number of pencils left unsold |
Packs of 3
|
Packs of 4
|
Total
|
Number |
10 u |
1 u |
|
Value |
3 |
4 |
|
Total value |
30 u |
4 u |
34 u |
Total number of pencils left unsold
= (10 u x 3) + (1 u x 4)
= 30 u + 4 u
= 34 u
34 u = 204
1 u = 204 ÷ 34 = 6
Number of packs of 4 sold
= (2 u - 1 u) + 18
= 1 u + 18
= 1 x 6 + 18
= 6 + 18
= 24
Answer(s): 24