Reggie and Ken collected some buttons. If Reggie gave Ken 62 buttons, both would have an equal number of buttons. If Ken gave Reggie 34 buttons, Reggie would have 4 times as many buttons as Ken. Find the number of buttons each of them had.
- Reggie?
- Ken?
| Case 1 |
Case 2 |
| Reggie |
Ken |
Reggie |
Ken |
| 5 u + 62 |
5 u - 62 |
8 u - 34 |
2 u + 34 |
| - 62 |
+ 62 |
+ 34 |
- 34 |
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 Ken had at first is the same in both cases.
5 u - 62 = 2 u + 34
5 u - 2 u = 62 + 34
3 u = 96
1 u = 96 ÷ 3 = 32
Number of buttons that Reggie had
= 5 u + 62
= 5 x 32 + 62
= 222
(b)
Number of buttons that Ken had
= 5 u - 62
= 5 x 32 - 62
= 98
Answer(s): (a) 222; (b) 98
