George and John collected some marbles. If George gave John 70 marbles, both would have an equal number of marbles. If John gave George 44 marbles, George would have 5 times as many marbles as John. Find the number of marbles each of them had.
- George?
- John?
| Case 1 |
Case 2 |
| George |
John |
George |
John |
| 3 u + 70 |
3 u - 70 |
5 u - 44 |
1 u + 44 |
| - 70 |
+ 70 |
+ 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 John had at first is the same in both cases.
3 u - 70 = 1 u + 44
3 u - 1 u = 70 + 44
2 u = 114
1 u = 114 ÷ 2 = 57
Number of marbles that George had
= 3 u + 70
= 3 x 57 + 70
= 241
(b)
Number of marbles that John had
= 3 u - 70
= 3 x 57 - 70
= 101
Answer(s): (a) 241; (b) 101
