Archie and Howard collected some stamps. If Archie gave Howard 62 stamps, both would have an equal number of stamps. If Howard gave Archie 40 stamps, Archie would have 5 times as many stamps as Howard. Find the number of stamps each of them had.
- Archie?
- Howard?
| Case 1 |
Case 2 |
| Archie |
Howard |
Archie |
Howard |
| 3 u + 62 |
3 u - 62 |
5 u - 40 |
1 u + 40 |
| - 62 |
+ 62 |
+ 40 |
- 40 |
1x3 =
3 u |
1x3 =
3 u |
5x1 =
5 u |
1x1 =
1 u |
(a)
The total number of stamps remains unchanged in both cases. Make the total number of stamps the same. LCM of 2 and 6 is 6.
The number of stamps that Howard had at first is the same in both cases.
3 u - 62 = 1 u + 40
3 u - 1 u = 62 + 40
2 u = 102
1 u = 102 ÷ 2 = 51
Number of stamps that Archie had
= 3 u + 62
= 3 x 51 + 62
= 215
(b)
Number of stamps that Howard had
= 3 u - 62
= 3 x 51 - 62
= 91
Answer(s): (a) 215; (b) 91
