Ivan and Peter collected some stamps. If Ivan gave Peter 59 stamps, both would have an equal number of stamps. If Peter gave Ivan 37 stamps, Ivan would have 5 times as many stamps as Peter. Find the number of stamps each of them had.
- Ivan?
- Peter?
| Case 1 |
Case 2 |
| Ivan |
Peter |
Ivan |
Peter |
| 3 u + 59 |
3 u - 59 |
5 u - 37 |
1 u + 37 |
| - 59 |
+ 59 |
+ 37 |
- 37 |
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 Peter had at first is the same in both cases.
3 u - 59 = 1 u + 37
3 u - 1 u = 59 + 37
2 u = 96
1 u = 96 ÷ 2 = 48
Number of stamps that Ivan had
= 3 u + 59
= 3 x 48 + 59
= 203
(b)
Number of stamps that Peter had
= 3 u - 59
= 3 x 48 - 59
= 85
Answer(s): (a) 203; (b) 85
