Mark and David collected some beads. If Mark gave David 51 beads, both would have an equal number of beads. If David gave Mark 45 beads, Mark would have 5 times as many beads as David. Find the number of beads each of them had.
- Mark?
- David?
| Case 1 |
Case 2 |
| Mark |
David |
Mark |
David |
| 3 u + 51 |
3 u - 51 |
5 u - 45 |
1 u + 45 |
| - 51 |
+ 51 |
+ 45 |
- 45 |
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 David had at first is the same in both cases.
3 u - 51 = 1 u + 45
3 u - 1 u = 51 + 45
2 u = 96
1 u = 96 ÷ 2 = 48
Number of beads that Mark had
= 3 u + 51
= 3 x 48 + 51
= 195
(b)
Number of beads that David had
= 3 u - 51
= 3 x 48 - 51
= 93
Answer(s): (a) 195; (b) 93
