Carl and Neave collected some cards. If Carl gave Neave 59 cards, both would have an equal number of cards. If Neave gave Carl 45 cards, Carl would have 5 times as many cards as Neave. Find the number of cards each of them had.
- Carl?
- Neave?
| Case 1 |
Case 2 |
| Carl |
Neave |
Carl |
Neave |
| 3 u + 59 |
3 u - 59 |
5 u - 45 |
1 u + 45 |
| - 59 |
+ 59 |
+ 45 |
- 45 |
1x3 =
3 u |
1x3 =
3 u |
5x1 =
5 u |
1x1 =
1 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of cards the same. LCM of 2 and 6 is 6.
The number of cards that Neave had at first is the same in both cases.
3 u - 59 = 1 u + 45
3 u - 1 u = 59 + 45
2 u = 104
1 u = 104 ÷ 2 = 52
Number of cards that Carl had
= 3 u + 59
= 3 x 52 + 59
= 215
(b)
Number of cards that Neave had
= 3 u - 59
= 3 x 52 - 59
= 97
Answer(s): (a) 215; (b) 97
