Ken and Reggie collected some buttons. If Ken gave Reggie 54 buttons, both would have an equal number of buttons. If Reggie gave Ken 40 buttons, Ken would have 5 times as many buttons as Reggie. Find the number of buttons each of them had.
- Ken?
- Reggie?
| Case 1 |
Case 2 |
| Ken |
Reggie |
Ken |
Reggie |
| 3 u + 54 |
3 u - 54 |
5 u - 40 |
1 u + 40 |
| - 54 |
+ 54 |
+ 40 |
- 40 |
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 buttons the same. LCM of 2 and 6 is 6.
The number of buttons that Reggie had at first is the same in both cases.
3 u - 54 = 1 u + 40
3 u - 1 u = 54 + 40
2 u = 94
1 u = 94 ÷ 2 = 47
Number of buttons that Ken had
= 3 u + 54
= 3 x 47 + 54
= 195
(b)
Number of buttons that Reggie had
= 3 u - 54
= 3 x 47 - 54
= 87
Answer(s): (a) 195; (b) 87
