Luis and David had some buttons in the ratio of 7 : 4. David and Owen had some buttons in the ratio of 3 : 1. Luis sold 30 buttons to Owen and ended up with half the number of buttons David had. How many buttons did Owen have in the end?
| Luis |
David |
Owen |
| 7x3 |
4x3 |
|
| |
3x4 |
1x4 |
| 21 u |
12 u |
4 u |
The number of buttons that David had at first is repeated. Make the number of buttons that David had at first the same. LCM of 4 and 3 is 12.
| |
Luis |
David |
Owen |
| Before |
21 u |
12 u |
4 u |
| Change |
- 30 |
|
+ 30 |
| After |
6 u |
12 u |
4 u + 30 |
Number of buttons that Luis had in the end
= 12 u ÷ 2
= 6 u
Number of buttons that Luis sold to Owen
= 21 u - 6 u
= 15 u
15 u = 30
1 u = 30 ÷ 15 = 2
Number of buttons that Owen had in the end
= 4 u + 30
= 4 x 2 + 30
= 8 + 30
= 38
Answer(s): 38
