Gabriel and Rael had some buttons in the ratio of 5 : 3. Rael and Xavier had some buttons in the ratio of 2 : 1. Gabriel sold 56 buttons to Xavier and ended up with half the number of buttons Rael had. How many buttons did Xavier have in the end?
| Gabriel |
Rael |
Xavier |
| 5x2 |
3x2 |
|
| |
2x3 |
1x3 |
| 10 u |
6 u |
3 u |
The number of buttons that Rael had at first is repeated. Make the number of buttons that Rael had at first the same. LCM of 3 and 2 is 6.
| |
Gabriel |
Rael |
Xavier |
| Before |
10 u |
6 u |
3 u |
| Change |
- 56 |
|
+ 56 |
| After |
3 u |
6 u |
3 u + 56 |
Number of buttons that Gabriel had in the end
= 6 u ÷ 2
= 3 u
Number of buttons that Gabriel sold to Xavier
= 10 u - 3 u
= 7 u
7 u = 56
1 u = 56 ÷ 7 = 8
Number of buttons that Xavier had in the end
= 3 u + 56
= 3 x 8 + 56
= 24 + 56
= 80
Answer(s): 80
