A bookshop sells pens in packs of 4 and 5. At first, there were 8 times as many packs of 4 as packs of 5. After selling half of the packs of 4 and some packs of 5, Mr Choy packs 13 additional packs of 5. How many packs of 4 are sold if there are 8 times as many packs of 4 as packs of 5 and there is a total of 259 unsold pens?
| |
Packs of 4 |
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 |
|
+ 13 |
| 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 8 is 16.
Number of pens
left unsold |
Packs of 4
|
Packs of 5
|
Total
|
| Number |
8 u |
1 u |
|
| Value |
4 |
5 |
|
| Total value |
32 u |
5 u |
37 u |
Total number of pens left unsold
= (8 u x 4) + (1 u x 5)
= 32 u + 5 u
= 37 u
37 u = 259
1 u = 259 ÷ 37 = 7
Number of packs of 5 sold
= (2 u - 1 u) + 13
= 1 u + 13
= 1 x 7 + 13
= 7 + 13
= 20
Answer(s): 20
