Luke and Eric had some buttons in the ratio of 6 : 5. Eric and John had some buttons in the ratio of 2 : 1. Luke sold 28 buttons to John and ended up with half the number of buttons Eric had. How many buttons did John have in the end?
| Luke |
Eric |
John |
| 6x2 |
5x2 |
|
| |
2x5 |
1x5 |
| 12 u |
10 u |
5 u |
The number of buttons that Eric had at first is repeated. Make the number of buttons that Eric had at first the same. LCM of 5 and 2 is 10.
| |
Luke |
Eric |
John |
| Before |
12 u |
10 u |
5 u |
| Change |
- 28 |
|
+ 28 |
| After |
5 u |
10 u |
5 u + 28 |
Number of buttons that Luke had in the end
= 10 u ÷ 2
= 5 u
Number of buttons that Luke sold to John
= 12 u - 5 u
= 7 u
7 u = 28
1 u = 28 ÷ 7 = 4
Number of buttons that John had in the end
= 5 u + 28
= 5 x 4 + 28
= 20 + 28
= 48
Answer(s): 48
