Pierre and Asher collected some beads. If Pierre gave Asher 52 beads, both would have an equal number of beads. If Asher gave Pierre 36 beads, Pierre would have 5 times as many beads as Asher. Find the number of beads each of them had.
- Pierre?
- Asher?
| Case 1 |
Case 2 |
| Pierre |
Asher |
Pierre |
Asher |
| 3 u + 52 |
3 u - 52 |
5 u - 36 |
1 u + 36 |
| - 52 |
+ 52 |
+ 36 |
- 36 |
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 Asher had at first is the same in both cases.
3 u - 52 = 1 u + 36
3 u - 1 u = 52 + 36
2 u = 88
1 u = 88 ÷ 2 = 44
Number of beads that Pierre had
= 3 u + 52
= 3 x 44 + 52
= 184
(b)
Number of beads that Asher had
= 3 u - 52
= 3 x 44 - 52
= 80
Answer(s): (a) 184; (b) 80
