Simon and Tim collected some marbles. If Simon gave Tim 59 marbles, both would have an equal number of marbles. If Tim gave Simon 37 marbles, Simon would have 4 times as many marbles as Tim. Find the number of marbles each of them had.
- Simon?
- Tim?
| Case 1 |
Case 2 |
| Simon |
Tim |
Simon |
Tim |
| 5 u + 59 |
5 u - 59 |
8 u - 37 |
2 u + 37 |
| - 59 |
+ 59 |
+ 37 |
- 37 |
1x5 =
5 u |
1x5 =
5 u |
4x2 =
8 u |
1x2 =
2 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of marbles the same. LCM of 2 and 5 is 10.
The number of marbles that Tim had at first is the same in both cases.
5 u - 59 = 2 u + 37
5 u - 2 u = 59 + 37
3 u = 96
1 u = 96 ÷ 3 = 32
Number of marbles that Simon had
= 5 u + 59
= 5 x 32 + 59
= 219
(b)
Number of marbles that Tim had
= 5 u - 59
= 5 x 32 - 59
= 101
Answer(s): (a) 219; (b) 101
