Tim and Will collected some beads. If Tim gave Will 51 beads, both would have an equal number of beads. If Will gave Tim 31 beads, Tim would have 5 times as many beads as Will. Find the number of beads each of them had.
- Tim?
- Will?
| Case 1 |
Case 2 |
| Tim |
Will |
Tim |
Will |
| 3 u + 51 |
3 u - 51 |
5 u - 31 |
1 u + 31 |
| - 51 |
+ 51 |
+ 31 |
- 31 |
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 Will had at first is the same in both cases.
3 u - 51 = 1 u + 31
3 u - 1 u = 51 + 31
2 u = 82
1 u = 82 ÷ 2 = 41
Number of beads that Tim had
= 3 u + 51
= 3 x 41 + 51
= 174
(b)
Number of beads that Will had
= 3 u - 51
= 3 x 41 - 51
= 72
Answer(s): (a) 174; (b) 72
