Warren and Archie collected some cards. If Warren gave Archie 61 cards, both would have an equal number of cards. If Archie gave Warren 34 cards, Warren would have 6 times as many cards as Archie. Find the number of cards each of them had.
- Warren?
- Archie?
| Case 1 |
Case 2 |
| Warren |
Archie |
Warren |
Archie |
| 7 u + 61 |
7 u - 61 |
12 u - 34 |
2 u + 34 |
| - 61 |
+ 61 |
+ 34 |
- 34 |
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 Archie had at first is the same in both cases.
7 u - 61 = 2 u + 34
7 u - 2 u = 61 + 34
5 u = 95
1 u = 95 ÷ 5 = 19
Number of cards that Warren had
= 7 u + 61
= 7 x 19 + 61
= 194
(b)
Number of cards that Archie had
= 7 u - 61
= 7 x 19 - 61
= 72
Answer(s): (a) 194; (b) 72
