Tom and Vaidev collected some coins. If Tom gave Vaidev 61 coins, both would have an equal number of coins. If Vaidev gave Tom 44 coins, Tom would have 4 times as many coins as Vaidev. Find the number of coins each of them had.
- Tom?
- Vaidev?
| Case 1 |
Case 2 |
| Tom |
Vaidev |
Tom |
Vaidev |
| 5 u + 61 |
5 u - 61 |
8 u - 44 |
2 u + 44 |
| - 61 |
+ 61 |
+ 44 |
- 44 |
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 Vaidev had at first is the same in both cases.
5 u - 61 = 2 u + 44
5 u - 2 u = 61 + 44
3 u = 105
1 u = 105 ÷ 3 = 35
Number of coins that Tom had
= 5 u + 61
= 5 x 35 + 61
= 236
(b)
Number of coins that Vaidev had
= 5 u - 61
= 5 x 35 - 61
= 114
Answer(s): (a) 236; (b) 114
