Rael and John collected some beads. If Rael gave John 70 beads, both would have an equal number of beads. If John gave Rael 38 beads, Rael would have 5 times as many beads as John. Find the number of beads each of them had.
- Rael?
- John?
| Case 1 |
Case 2 |
| Rael |
John |
Rael |
John |
| 3 u + 70 |
3 u - 70 |
5 u - 38 |
1 u + 38 |
| - 70 |
+ 70 |
+ 38 |
- 38 |
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 John had at first is the same in both cases.
3 u - 70 = 1 u + 38
3 u - 1 u = 70 + 38
2 u = 108
1 u = 108 ÷ 2 = 54
Number of beads that Rael had
= 3 u + 70
= 3 x 54 + 70
= 232
(b)
Number of beads that John had
= 3 u - 70
= 3 x 54 - 70
= 92
Answer(s): (a) 232; (b) 92
