Archie and Simon collected some stickers. If Archie gave Simon 55 stickers, both would have an equal number of stickers. If Simon gave Archie 32 stickers, Archie would have 4 times as many stickers as Simon. Find the number of stickers each of them had.
- Archie?
- Simon?
| Case 1 |
Case 2 |
| Archie |
Simon |
Archie |
Simon |
| 5 u + 55 |
5 u - 55 |
8 u - 32 |
2 u + 32 |
| - 55 |
+ 55 |
+ 32 |
- 32 |
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 stickers the same. LCM of 2 and 5 is 10.
The number of stickers that Simon had at first is the same in both cases.
5 u - 55 = 2 u + 32
5 u - 2 u = 55 + 32
3 u = 87
1 u = 87 ÷ 3 = 29
Number of stickers that Archie had
= 5 u + 55
= 5 x 29 + 55
= 200
(b)
Number of stickers that Simon had
= 5 u - 55
= 5 x 29 - 55
= 90
Answer(s): (a) 200; (b) 90
