Ahmad and Harry collected some stamps. If Ahmad gave Harry 60 stamps, both would have an equal number of stamps. If Harry gave Ahmad 33 stamps, Ahmad would have 4 times as many stamps as Harry. Find the number of stamps each of them had.
- Ahmad?
- Harry?
| Case 1 |
Case 2 |
| Ahmad |
Harry |
Ahmad |
Harry |
| 5 u + 60 |
5 u - 60 |
8 u - 33 |
2 u + 33 |
| - 60 |
+ 60 |
+ 33 |
- 33 |
1x5 =
5 u |
1x5 =
5 u |
4x2 =
8 u |
1x2 =
2 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of stamps the same. LCM of 2 and 5 is 10.
The number of stamps that Harry had at first is the same in both cases.
5 u - 60 = 2 u + 33
5 u - 2 u = 60 + 33
3 u = 93
1 u = 93 ÷ 3 = 31
Number of stamps that Ahmad had
= 5 u + 60
= 5 x 31 + 60
= 215
(b)
Number of stamps that Harry had
= 5 u - 60
= 5 x 31 - 60
= 95
Answer(s): (a) 215; (b) 95
