A stationery booth sells notebooks in packs of 5 and 7. At first, there were 10 times as many packs of 5 as packs of 7. After selling half of the packs of 5 and some packs of 7, Mr Yong packs 18 additional packs of 7. How many packs of 5 and 7 are sold if there are 10 times as many packs of 5 as packs of 7 and there is a total of 285 unsold notebooks?
| |
Packs of 5 |
Packs of 7 |
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 5 in the end is repeated. Make the number of packs of 5 in the end the same. LCM of 1 and 10 is 10.
The number of packs of 5 at first is repeated. Make the number of packs of 5 at first the same. LCM of 20 and 10 is 20.
Number of notebooks
left unsold |
Packs of 5
|
Packs of 7
|
Total
|
| Number |
10 u |
1 u |
|
| Value |
5 |
7 |
|
| Total value |
50 u |
7 u |
57 u |
Total number of notebooks left unsold
= (10 u x 5) + (1 u x 7)
= 50 u + 7 u
= 57 u
57 u = 285
1 u = 285 ÷ 57 = 5
Number of packs of 5 and 7 sold
= 10 u + (2 u - 1 u) + 18
= 10 u + 1 u + 18
= 11 u + 18
= 11 x 5 + 18
= 55 + 18
= 73
Answer(s): 73
