Archie and Fabian collected some marbles. If Archie gave Fabian 64 marbles, both would have an equal number of marbles. If Fabian gave Archie 34 marbles, Archie would have 5 times as many marbles as Fabian. Find the number of marbles each of them had.
- Archie?
- Fabian?
| Case 1 |
Case 2 |
| Archie |
Fabian |
Archie |
Fabian |
| 3 u + 64 |
3 u - 64 |
5 u - 34 |
1 u + 34 |
| - 64 |
+ 64 |
+ 34 |
- 34 |
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 marbles the same. LCM of 2 and 6 is 6.
The number of marbles that Fabian had at first is the same in both cases.
3 u - 64 = 1 u + 34
3 u - 1 u = 64 + 34
2 u = 98
1 u = 98 ÷ 2 = 49
Number of marbles that Archie had
= 3 u + 64
= 3 x 49 + 64
= 211
(b)
Number of marbles that Fabian had
= 3 u - 64
= 3 x 49 - 64
= 83
Answer(s): (a) 211; (b) 83
