Ken and Ahmad collected some buttons. If Ken gave Ahmad 63 buttons, both would have an equal number of buttons. If Ahmad gave Ken 41 buttons, Ken would have 5 times as many buttons as Ahmad. Find the number of buttons each of them had.
- Ken?
- Ahmad?
| Case 1 |
Case 2 |
| Ken |
Ahmad |
Ken |
Ahmad |
| 3 u + 63 |
3 u - 63 |
5 u - 41 |
1 u + 41 |
| - 63 |
+ 63 |
+ 41 |
- 41 |
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 Ahmad had at first is the same in both cases.
3 u - 63 = 1 u + 41
3 u - 1 u = 63 + 41
2 u = 104
1 u = 104 ÷ 2 = 52
Number of buttons that Ken had
= 3 u + 63
= 3 x 52 + 63
= 219
(b)
Number of buttons that Ahmad had
= 3 u - 63
= 3 x 52 - 63
= 93
Answer(s): (a) 219; (b) 93
