Ian and Ivan collected some stamps. If Ian gave Ivan 53 stamps, both would have an equal number of stamps. If Ivan gave Ian 37 stamps, Ian would have 4 times as many stamps as Ivan. Find the number of stamps each of them had.
- Ian?
- Ivan?
| Case 1 |
Case 2 |
| Ian |
Ivan |
Ian |
Ivan |
| 5 u + 53 |
5 u - 53 |
8 u - 37 |
2 u + 37 |
| - 53 |
+ 53 |
+ 37 |
- 37 |
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 stamps the same. LCM of 2 and 5 is 10.
The number of stamps that Ivan had at first is the same in both cases.
5 u - 53 = 2 u + 37
5 u - 2 u = 53 + 37
3 u = 90
1 u = 90 ÷ 3 = 30
Number of stamps that Ian had
= 5 u + 53
= 5 x 30 + 53
= 203
(b)
Number of stamps that Ivan had
= 5 u - 53
= 5 x 30 - 53
= 97
Answer(s): (a) 203; (b) 97
