Paul and Albert collected some buttons. If Paul gave Albert 57 buttons, both would have an equal number of buttons. If Albert gave Paul 33 buttons, Paul would have 4 times as many buttons as Albert. Find the number of buttons each of them had.
- Paul?
- Albert?
| Case 1 |
Case 2 |
| Paul |
Albert |
Paul |
Albert |
| 5 u + 57 |
5 u - 57 |
8 u - 33 |
2 u + 33 |
| - 57 |
+ 57 |
+ 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 buttons the same. LCM of 2 and 5 is 10.
The number of buttons that Albert had at first is the same in both cases.
5 u - 57 = 2 u + 33
5 u - 2 u = 57 + 33
3 u = 90
1 u = 90 ÷ 3 = 30
Number of buttons that Paul had
= 5 u + 57
= 5 x 30 + 57
= 207
(b)
Number of buttons that Albert had
= 5 u - 57
= 5 x 30 - 57
= 93
Answer(s): (a) 207; (b) 93
