Ivan and Bobby collected some cards. If Ivan gave Bobby 68 cards, both would have an equal number of cards. If Bobby gave Ivan 43 cards, Ivan would have 4 times as many cards as Bobby. Find the number of cards each of them had.
- Ivan?
- Bobby?
| Case 1 |
Case 2 |
| Ivan |
Bobby |
Ivan |
Bobby |
| 5 u + 68 |
5 u - 68 |
8 u - 43 |
2 u + 43 |
| - 68 |
+ 68 |
+ 43 |
- 43 |
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 Bobby had at first is the same in both cases.
5 u - 68 = 2 u + 43
5 u - 2 u = 68 + 43
3 u = 111
1 u = 111 ÷ 3 = 37
Number of cards that Ivan had
= 5 u + 68
= 5 x 37 + 68
= 253
(b)
Number of cards that Bobby had
= 5 u - 68
= 5 x 37 - 68
= 117
Answer(s): (a) 253; (b) 117
