Simon and Jack collected some coins. If Simon gave Jack 69 coins, both would have an equal number of coins. If Jack gave Simon 36 coins, Simon would have 6 times as many coins as Jack. Find the number of coins each of them had.
- Simon?
- Jack?
| Case 1 |
Case 2 |
| Simon |
Jack |
Simon |
Jack |
| 7 u + 69 |
7 u - 69 |
12 u - 36 |
2 u + 36 |
| - 69 |
+ 69 |
+ 36 |
- 36 |
1x7 =
7 u |
1x7 =
7 u |
6x2 =
12 u |
1x2 =
2 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of coins the same. LCM of 2 and 7 is 14.
The number of coins that Jack had at first is the same in both cases.
7 u - 69 = 2 u + 36
7 u - 2 u = 69 + 36
5 u = 105
1 u = 105 ÷ 5 = 21
Number of coins that Simon had
= 7 u + 69
= 7 x 21 + 69
= 216
(b)
Number of coins that Jack had
= 7 u - 69
= 7 x 21 - 69
= 78
Answer(s): (a) 216; (b) 78
