Howard and Bobby collected some coins. If Howard gave Bobby 50 coins, both would have an equal number of coins. If Bobby gave Howard 34 coins, Howard would have 4 times as many coins as Bobby. Find the number of coins each of them had.
- Howard?
- Bobby?
| Case 1 |
Case 2 |
| Howard |
Bobby |
Howard |
Bobby |
| 5 u + 50 |
5 u - 50 |
8 u - 34 |
2 u + 34 |
| - 50 |
+ 50 |
+ 34 |
- 34 |
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 Bobby had at first is the same in both cases.
5 u - 50 = 2 u + 34
5 u - 2 u = 50 + 34
3 u = 84
1 u = 84 ÷ 3 = 28
Number of coins that Howard had
= 5 u + 50
= 5 x 28 + 50
= 190
(b)
Number of coins that Bobby had
= 5 u - 50
= 5 x 28 - 50
= 90
Answer(s): (a) 190; (b) 90
