A stationery kiosk sells pencils in packs of 5 and 7. At first, there were 8 times as many packs of 5 as packs of 7. After selling half of the packs of 5 and some packs of 7, Mr Ma packs 6 additional packs of 7. How many packs of 5 and 7 are sold if there are 8 times as many packs of 5 as packs of 7 and there is a total of 235 unsold pencils?
|
Packs of 5 |
Packs of 7 |
Comparing the number of packs at first |
8x2 = 16 u |
1x2 = 2 u |
Before |
2x8 = 16 u |
|
Change 1 |
- 1x8 = - 8 u |
- ? |
Change 2 |
|
+ 6 |
After |
1x8 = 8 u |
|
Comparing the number of packs in the end |
8 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 8 is 8.
The number of packs of 5 at first is repeated. Make the number of packs of 5 at first the same. LCM of 16 and 8 is 16.
Number of pencils left unsold |
Packs of 5
|
Packs of 7
|
Total
|
Number |
8 u |
1 u |
|
Value |
5 |
7 |
|
Total value |
40 u |
7 u |
47 u |
Total number of pencils left unsold
= (8 u x 5) + (1 u x 7)
= 40 u + 7 u
= 47 u
47 u = 235
1 u = 235 ÷ 47 = 5
Number of packs of 5 and 7 sold
= 8 u + (2 u - 1 u) + 6
= 8 u + 1 u + 6
= 9 u + 6
= 9 x 5 + 6
= 45 + 6
= 51
Answer(s): 51