Glen and Ethan collected some buttons. If Glen gave Ethan 61 buttons, both would have an equal number of buttons. If Ethan gave Glen 39 buttons, Glen would have 6 times as many buttons as Ethan. Find the number of buttons each of them had.
- Glen?
- Ethan?
| Case 1 |
Case 2 |
| Glen |
Ethan |
Glen |
Ethan |
| 7 u + 61 |
7 u - 61 |
12 u - 39 |
2 u + 39 |
| - 61 |
+ 61 |
+ 39 |
- 39 |
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 Ethan had at first is the same in both cases.
7 u - 61 = 2 u + 39
7 u - 2 u = 61 + 39
5 u = 100
1 u = 100 ÷ 5 = 20
Number of buttons that Glen had
= 7 u + 61
= 7 x 20 + 61
= 201
(b)
Number of buttons that Ethan had
= 7 u - 61
= 7 x 20 - 61
= 79
Answer(s): (a) 201; (b) 79
