Sean and Cody collected some beads. If Sean gave Cody 65 beads, both would have an equal number of beads. If Cody gave Sean 39 beads, Sean would have 5 times as many beads as Cody. Find the number of beads each of them had.
- Sean?
- Cody?
| Case 1 |
Case 2 |
| Sean |
Cody |
Sean |
Cody |
| 3 u + 65 |
3 u - 65 |
5 u - 39 |
1 u + 39 |
| - 65 |
+ 65 |
+ 39 |
- 39 |
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 Cody had at first is the same in both cases.
3 u - 65 = 1 u + 39
3 u - 1 u = 65 + 39
2 u = 104
1 u = 104 ÷ 2 = 52
Number of beads that Sean had
= 3 u + 65
= 3 x 52 + 65
= 221
(b)
Number of beads that Cody had
= 3 u - 65
= 3 x 52 - 65
= 91
Answer(s): (a) 221; (b) 91
