Asher and Gabriel had some buttons in the ratio of 9 : 5. Gabriel and Charlie had some buttons in the ratio of 2 : 1. Asher sold 78 buttons to Charlie and ended up with half the number of buttons Gabriel had. How many buttons did Charlie have in the end?
| Asher |
Gabriel |
Charlie |
| 9x2 |
5x2 |
|
| |
2x5 |
1x5 |
| 18 u |
10 u |
5 u |
The number of buttons that Gabriel had at first is repeated. Make the number of buttons that Gabriel had at first the same. LCM of 5 and 2 is 10.
| |
Asher |
Gabriel |
Charlie |
| Before |
18 u |
10 u |
5 u |
| Change |
- 78 |
|
+ 78 |
| After |
5 u |
10 u |
5 u + 78 |
Number of buttons that Asher had in the end
= 10 u ÷ 2
= 5 u
Number of buttons that Asher sold to Charlie
= 18 u - 5 u
= 13 u
13 u = 78
1 u = 78 ÷ 13 = 6
Number of buttons that Charlie had in the end
= 5 u + 78
= 5 x 6 + 78
= 30 + 78
= 108
Answer(s): 108
