Asher and Ahmad collected some buttons. If Asher gave Ahmad 64 buttons, both would have an equal number of buttons. If Ahmad gave Asher 41 buttons, Asher would have 6 times as many buttons as Ahmad. Find the number of buttons each of them had.
- Asher?
- Ahmad?
| Case 1 |
Case 2 |
| Asher |
Ahmad |
Asher |
Ahmad |
| 7 u + 64 |
7 u - 64 |
12 u - 41 |
2 u + 41 |
| - 64 |
+ 64 |
+ 41 |
- 41 |
1x7 =
7 u |
1x7 =
7 u |
6x2 =
12 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 7 is 14.
The number of buttons that Ahmad had at first is the same in both cases.
7 u - 64 = 2 u + 41
7 u - 2 u = 64 + 41
5 u = 105
1 u = 105 ÷ 5 = 21
Number of buttons that Asher had
= 7 u + 64
= 7 x 21 + 64
= 211
(b)
Number of buttons that Ahmad had
= 7 u - 64
= 7 x 21 - 64
= 83
Answer(s): (a) 211; (b) 83
