Billy and Fabian collected some cards. If Billy gave Fabian 66 cards, both would have an equal number of cards. If Fabian gave Billy 34 cards, Billy would have 6 times as many cards as Fabian. Find the number of cards each of them had.
- Billy?
- Fabian?
| Case 1 |
Case 2 |
| Billy |
Fabian |
Billy |
Fabian |
| 7 u + 66 |
7 u - 66 |
12 u - 34 |
2 u + 34 |
| - 66 |
+ 66 |
+ 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 Fabian had at first is the same in both cases.
7 u - 66 = 2 u + 34
7 u - 2 u = 66 + 34
5 u = 100
1 u = 100 ÷ 5 = 20
Number of cards that Billy had
= 7 u + 66
= 7 x 20 + 66
= 206
(b)
Number of cards that Fabian had
= 7 u - 66
= 7 x 20 - 66
= 74
Answer(s): (a) 206; (b) 74
