A bookshop sells markers in packs of 3 and 6. At first, there were 8 times as many packs of 3 as packs of 6. After selling half of the packs of 3 and some packs of 6, Mr Seow packs 17 additional packs of 6. How many packs of 3 and 6 are sold if there are 8 times as many packs of 3 as packs of 6 and there is a total of 240 unsold markers?
|
Packs of 3 |
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 |
|
+ 17 |
After |
1x8 = 8 u |
|
Comparing the number of packs in the end |
8 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 8 is 8.
The number of packs of 3 at first is repeated. Make the number of packs of 3 at first the same. LCM of 16 and 8 is 16.
Number of markers left unsold |
Packs of 3
|
Packs of 6
|
Total
|
Number |
8 u |
1 u |
|
Value |
3 |
6 |
|
Total value |
24 u |
6 u |
30 u |
Total number of markers left unsold
= (8 u x 3) + (1 u x 6)
= 24 u + 6 u
= 30 u
30 u = 240
1 u = 240 ÷ 30 = 8
Number of packs of 3 and 6 sold
= 8 u + (2 u - 1 u) + 17
= 8 u + 1 u + 17
= 9 u + 17
= 9 x 8 + 17
= 72 + 17
= 89
Answer(s): 89