Zeph and Fred collected some stamps. If Zeph gave Fred 68 stamps, both would have an equal number of stamps. If Fred gave Zeph 37 stamps, Zeph would have 4 times as many stamps as Fred. Find the number of stamps each of them had.
- Zeph?
- Fred?
| Case 1 |
Case 2 |
| Zeph |
Fred |
Zeph |
Fred |
| 5 u + 68 |
5 u - 68 |
8 u - 37 |
2 u + 37 |
| - 68 |
+ 68 |
+ 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 Fred had at first is the same in both cases.
5 u - 68 = 2 u + 37
5 u - 2 u = 68 + 37
3 u = 105
1 u = 105 ÷ 3 = 35
Number of stamps that Zeph had
= 5 u + 68
= 5 x 35 + 68
= 243
(b)
Number of stamps that Fred had
= 5 u - 68
= 5 x 35 - 68
= 107
Answer(s): (a) 243; (b) 107
