Archie and Billy collected some buttons. If Archie gave Billy 70 buttons, both would have an equal number of buttons. If Billy gave Archie 35 buttons, Archie would have 6 times as many buttons as Billy. Find the number of buttons each of them had.
- Archie?
- Billy?
| Case 1 |
Case 2 |
| Archie |
Billy |
Archie |
Billy |
| 7 u + 70 |
7 u - 70 |
12 u - 35 |
2 u + 35 |
| - 70 |
+ 70 |
+ 35 |
- 35 |
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 Billy had at first is the same in both cases.
7 u - 70 = 2 u + 35
7 u - 2 u = 70 + 35
5 u = 105
1 u = 105 ÷ 5 = 21
Number of buttons that Archie had
= 7 u + 70
= 7 x 21 + 70
= 217
(b)
Number of buttons that Billy had
= 7 u - 70
= 7 x 21 - 70
= 77
Answer(s): (a) 217; (b) 77
