Ken and Simon collected some marbles. If Ken gave Simon 63 marbles, both would have an equal number of marbles. If Simon gave Ken 31 marbles, Ken would have 5 times as many marbles as Simon. Find the number of marbles each of them had.
- Ken?
- Simon?
| Case 1 |
Case 2 |
| Ken |
Simon |
Ken |
Simon |
| 3 u + 63 |
3 u - 63 |
5 u - 31 |
1 u + 31 |
| - 63 |
+ 63 |
+ 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 marbles the same. LCM of 2 and 6 is 6.
The number of marbles that Simon had at first is the same in both cases.
3 u - 63 = 1 u + 31
3 u - 1 u = 63 + 31
2 u = 94
1 u = 94 ÷ 2 = 47
Number of marbles that Ken had
= 3 u + 63
= 3 x 47 + 63
= 204
(b)
Number of marbles that Simon had
= 3 u - 63
= 3 x 47 - 63
= 78
Answer(s): (a) 204; (b) 78
