Mark and Seth collected some beads. If Mark gave Seth 68 beads, both would have an equal number of beads. If Seth gave Mark 30 beads, Mark would have 5 times as many beads as Seth. Find the number of beads each of them had.
- Mark?
- Seth?
| Case 1 |
Case 2 |
| Mark |
Seth |
Mark |
Seth |
| 3 u + 68 |
3 u - 68 |
5 u - 30 |
1 u + 30 |
| - 68 |
+ 68 |
+ 30 |
- 30 |
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 beads the same. LCM of 2 and 6 is 6.
The number of beads that Seth had at first is the same in both cases.
3 u - 68 = 1 u + 30
3 u - 1 u = 68 + 30
2 u = 98
1 u = 98 ÷ 2 = 49
Number of beads that Mark had
= 3 u + 68
= 3 x 49 + 68
= 215
(b)
Number of beads that Seth had
= 3 u - 68
= 3 x 49 - 68
= 79
Answer(s): (a) 215; (b) 79
