Simon and Ian collected some cards. If Simon gave Ian 56 cards, both would have an equal number of cards. If Ian gave Simon 39 cards, Simon would have 6 times as many cards as Ian. Find the number of cards each of them had.
- Simon?
- Ian?
| Case 1 |
Case 2 |
| Simon |
Ian |
Simon |
Ian |
| 7 u + 56 |
7 u - 56 |
12 u - 39 |
2 u + 39 |
| - 56 |
+ 56 |
+ 39 |
- 39 |
1x7 =
7 u |
1x7 =
7 u |
6x2 =
12 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 7 is 14.
The number of cards that Ian had at first is the same in both cases.
7 u - 56 = 2 u + 39
7 u - 2 u = 56 + 39
5 u = 95
1 u = 95 ÷ 5 = 19
Number of cards that Simon had
= 7 u + 56
= 7 x 19 + 56
= 189
(b)
Number of cards that Ian had
= 7 u - 56
= 7 x 19 - 56
= 77
Answer(s): (a) 189; (b) 77
