Liam and Ryan collected some coins. If Liam gave Ryan 57 coins, both would have an equal number of coins. If Ryan gave Liam 39 coins, Liam would have 4 times as many coins as Ryan. Find the number of coins each of them had.
- Liam?
- Ryan?
| Case 1 |
Case 2 |
| Liam |
Ryan |
Liam |
Ryan |
| 5 u + 57 |
5 u - 57 |
8 u - 39 |
2 u + 39 |
| - 57 |
+ 57 |
+ 39 |
- 39 |
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 coins the same. LCM of 2 and 5 is 10.
The number of coins that Ryan had at first is the same in both cases.
5 u - 57 = 2 u + 39
5 u - 2 u = 57 + 39
3 u = 96
1 u = 96 ÷ 3 = 32
Number of coins that Liam had
= 5 u + 57
= 5 x 32 + 57
= 217
(b)
Number of coins that Ryan had
= 5 u - 57
= 5 x 32 - 57
= 103
Answer(s): (a) 217; (b) 103
