A bookstore sells staplers in packs of 4 and 7. At first, there were 4 times as many packs of 4 as packs of 7. After selling half of the packs of 4 and some packs of 7, Mr Chong packs 14 additional packs of 7. How many packs of 4 are sold if there are 8 times as many packs of 4 as packs of 7 and there is a total of 117 unsold staplers?
| |
Packs of 4 |
Packs of 7 |
Comparing the number
of packs at first |
4x4 =
16 u |
1x4 =
4 u |
| Before |
2x8 =
16 u |
|
| Change 1 |
- 1x8 =
- 8 u |
- ? |
| Change 2 |
|
+ 14 |
| After |
1x8 =
8 u |
|
Comparing the number
of packs in the end |
8 u |
1 u |
The number of packs of 4 in the end is repeated. Make the number of packs of 4 in the end the same. LCM of 1 and 8 is 8.
The number of packs of 4 at first is repeated. Make the number of packs of 4 at first the same. LCM of 16 and 4 is 16.
Number of staplers
left unsold |
Packs of 4
|
Packs of 7
|
Total
|
| Number |
8 u |
1 u |
|
| Value |
4 |
7 |
|
| Total value |
32 u |
7 u |
39 u |
Total number of staplers left unsold
= (8 u x 4) + (1 u x 7)
= 32 u + 7 u
= 39 u
39 u = 117
1 u = 117 ÷ 39 = 3
Number of packs of 7 sold
= (4 u - 1 u) + 14
= 3 u + 14
= 3 x 3 + 14
= 9 + 14
= 23
Answer(s): 23
