Bryan and Fabian collected some cards. If Bryan gave Fabian 58 cards, both would have an equal number of cards. If Fabian gave Bryan 38 cards, Bryan would have 5 times as many cards as Fabian. Find the number of cards each of them had.
- Bryan?
- Fabian?
| Case 1 |
Case 2 |
| Bryan |
Fabian |
Bryan |
Fabian |
| 3 u + 58 |
3 u - 58 |
5 u - 38 |
1 u + 38 |
| - 58 |
+ 58 |
+ 38 |
- 38 |
1x3 =
3 u |
1x3 =
3 u |
5x1 =
5 u |
1x1 =
1 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of cards the same. LCM of 2 and 6 is 6.
The number of cards that Fabian had at first is the same in both cases.
3 u - 58 = 1 u + 38
3 u - 1 u = 58 + 38
2 u = 96
1 u = 96 ÷ 2 = 48
Number of cards that Bryan had
= 3 u + 58
= 3 x 48 + 58
= 202
(b)
Number of cards that Fabian had
= 3 u - 58
= 3 x 48 - 58
= 86
Answer(s): (a) 202; (b) 86
