Albert and Reggie collected some stamps. If Albert gave Reggie 66 stamps, both would have an equal number of stamps. If Reggie gave Albert 33 stamps, Albert would have 4 times as many stamps as Reggie. Find the number of stamps each of them had.
- Albert?
- Reggie?
| Case 1 |
Case 2 |
| Albert |
Reggie |
Albert |
Reggie |
| 5 u + 66 |
5 u - 66 |
8 u - 33 |
2 u + 33 |
| - 66 |
+ 66 |
+ 33 |
- 33 |
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 Reggie had at first is the same in both cases.
5 u - 66 = 2 u + 33
5 u - 2 u = 66 + 33
3 u = 99
1 u = 99 ÷ 3 = 33
Number of stamps that Albert had
= 5 u + 66
= 5 x 33 + 66
= 231
(b)
Number of stamps that Reggie had
= 5 u - 66
= 5 x 33 - 66
= 99
Answer(s): (a) 231; (b) 99
