Flynn and Liam collected some buttons. If Flynn gave Liam 60 buttons, both would have an equal number of buttons. If Liam gave Flynn 30 buttons, Flynn would have 4 times as many buttons as Liam. Find the number of buttons each of them had.
- Flynn?
- Liam?
| Case 1 |
Case 2 |
| Flynn |
Liam |
Flynn |
Liam |
| 5 u + 60 |
5 u - 60 |
8 u - 30 |
2 u + 30 |
| - 60 |
+ 60 |
+ 30 |
- 30 |
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 Liam had at first is the same in both cases.
5 u - 60 = 2 u + 30
5 u - 2 u = 60 + 30
3 u = 90
1 u = 90 ÷ 3 = 30
Number of buttons that Flynn had
= 5 u + 60
= 5 x 30 + 60
= 210
(b)
Number of buttons that Liam had
= 5 u - 60
= 5 x 30 - 60
= 90
Answer(s): (a) 210; (b) 90
