Fabian and Simon collected some stamps. If Fabian gave Simon 51 stamps, both would have an equal number of stamps. If Simon gave Fabian 34 stamps, Fabian would have 6 times as many stamps as Simon. Find the number of stamps each of them had.
- Fabian?
- Simon?
| Case 1 |
Case 2 |
| Fabian |
Simon |
Fabian |
Simon |
| 7 u + 51 |
7 u - 51 |
12 u - 34 |
2 u + 34 |
| - 51 |
+ 51 |
+ 34 |
- 34 |
1x7 =
7 u |
1x7 =
7 u |
6x2 =
12 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 7 is 14.
The number of stamps that Simon had at first is the same in both cases.
7 u - 51 = 2 u + 34
7 u - 2 u = 51 + 34
5 u = 85
1 u = 85 ÷ 5 = 17
Number of stamps that Fabian had
= 7 u + 51
= 7 x 17 + 51
= 170
(b)
Number of stamps that Simon had
= 7 u - 51
= 7 x 17 - 51
= 68
Answer(s): (a) 170; (b) 68
