Michael and Bobby collected some buttons. If Michael gave Bobby 56 buttons, both would have an equal number of buttons. If Bobby gave Michael 34 buttons, Michael would have 6 times as many buttons as Bobby. Find the number of buttons each of them had.
- Michael?
- Bobby?
| Case 1 |
Case 2 |
| Michael |
Bobby |
Michael |
Bobby |
| 7 u + 56 |
7 u - 56 |
12 u - 34 |
2 u + 34 |
| - 56 |
+ 56 |
+ 34 |
- 34 |
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 Bobby had at first is the same in both cases.
7 u - 56 = 2 u + 34
7 u - 2 u = 56 + 34
5 u = 90
1 u = 90 ÷ 5 = 18
Number of buttons that Michael had
= 7 u + 56
= 7 x 18 + 56
= 182
(b)
Number of buttons that Bobby had
= 7 u - 56
= 7 x 18 - 56
= 70
Answer(s): (a) 182; (b) 70
