Ian and Bobby collected some cards. If Ian gave Bobby 57 cards, both would have an equal number of cards. If Bobby gave Ian 33 cards, Ian would have 4 times as many cards as Bobby. Find the number of cards each of them had.
- Ian?
- Bobby?
| Case 1 |
Case 2 |
| Ian |
Bobby |
Ian |
Bobby |
| 5 u + 57 |
5 u - 57 |
8 u - 33 |
2 u + 33 |
| - 57 |
+ 57 |
+ 33 |
- 33 |
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 - 57 = 2 u + 33
5 u - 2 u = 57 + 33
3 u = 90
1 u = 90 ÷ 3 = 30
Number of cards that Ian had
= 5 u + 57
= 5 x 30 + 57
= 207
(b)
Number of cards that Bobby had
= 5 u - 57
= 5 x 30 - 57
= 93
Answer(s): (a) 207; (b) 93
