A stationery kiosk sells markers in packs of 3 and 5. At first, there were 8 times as many packs of 3 as packs of 5. After selling half of the packs of 3 and some packs of 5, Mr Lim packs 10 additional packs of 5. How many packs of 3 and 5 are sold if there are 8 times as many packs of 3 as packs of 5 and there is a total of 290 unsold markers?
| |
Packs of 3 |
Packs of 5 |
Comparing the number
of packs at first |
8x2 =
16 u |
1x2 =
2 u |
| Before |
2x8 =
16 u |
|
| Change 1 |
- 1x8 =
- 8 u |
- ? |
| Change 2 |
|
+ 10 |
| 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 5
|
Total
|
| Number |
8 u |
1 u |
|
| Value |
3 |
5 |
|
| Total value |
24 u |
5 u |
29 u |
Total number of markers left unsold
= (8 u x 3) + (1 u x 5)
= 24 u + 5 u
= 29 u
29 u = 290
1 u = 290 ÷ 29 = 10
Number of packs of 3 and 5 sold
= 8 u + (2 u - 1 u) + 10
= 8 u + 1 u + 10
= 9 u + 10
= 9 x 10 + 10
= 90 + 10
= 100
Answer(s): 100
