Peter and Oscar collected some cards. If Peter gave Oscar 55 cards, both would have an equal number of cards. If Oscar gave Peter 44 cards, Peter would have 4 times as many cards as Oscar. Find the number of cards each of them had.
- Peter?
- Oscar?
| Case 1 |
Case 2 |
| Peter |
Oscar |
Peter |
Oscar |
| 5 u + 55 |
5 u - 55 |
8 u - 44 |
2 u + 44 |
| - 55 |
+ 55 |
+ 44 |
- 44 |
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 - 55 = 2 u + 44
5 u - 2 u = 55 + 44
3 u = 99
1 u = 99 ÷ 3 = 33
Number of cards that Peter had
= 5 u + 55
= 5 x 33 + 55
= 220
(b)
Number of cards that Oscar had
= 5 u - 55
= 5 x 33 - 55
= 110
Answer(s): (a) 220; (b) 110
