Paul and Jeremy collected some marbles. If Paul gave Jeremy 68 marbles, both would have an equal number of marbles. If Jeremy gave Paul 44 marbles, Paul would have 5 times as many marbles as Jeremy. Find the number of marbles each of them had.
- Paul?
- Jeremy?
| Case 1 |
Case 2 |
| Paul |
Jeremy |
Paul |
Jeremy |
| 3 u + 68 |
3 u - 68 |
5 u - 44 |
1 u + 44 |
| - 68 |
+ 68 |
+ 44 |
- 44 |
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 marbles the same. LCM of 2 and 6 is 6.
The number of marbles that Jeremy had at first is the same in both cases.
3 u - 68 = 1 u + 44
3 u - 1 u = 68 + 44
2 u = 112
1 u = 112 ÷ 2 = 56
Number of marbles that Paul had
= 3 u + 68
= 3 x 56 + 68
= 236
(b)
Number of marbles that Jeremy had
= 3 u - 68
= 3 x 56 - 68
= 100
Answer(s): (a) 236; (b) 100
