Owen and Oscar collected some cards. If Owen gave Oscar 67 cards, both would have an equal number of cards. If Oscar gave Owen 38 cards, Owen would have 4 times as many cards as Oscar. Find the number of cards each of them had.
- Owen?
- Oscar?
| Case 1 |
Case 2 |
| Owen |
Oscar |
Owen |
Oscar |
| 5 u + 67 |
5 u - 67 |
8 u - 38 |
2 u + 38 |
| - 67 |
+ 67 |
+ 38 |
- 38 |
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 cards the same. LCM of 2 and 5 is 10.
The number of cards that Oscar had at first is the same in both cases.
5 u - 67 = 2 u + 38
5 u - 2 u = 67 + 38
3 u = 105
1 u = 105 ÷ 3 = 35
Number of cards that Owen had
= 5 u + 67
= 5 x 35 + 67
= 242
(b)
Number of cards that Oscar had
= 5 u - 67
= 5 x 35 - 67
= 108
Answer(s): (a) 242; (b) 108
