Eric and Riordan had some buttons in the ratio of 5 : 2. Riordan and Japheth had some buttons in the ratio of 5 : 1. Eric sold 140 buttons to Japheth and ended up with half the number of buttons Riordan had. How many buttons did Japheth have in the end?
| Eric |
Riordan |
Japheth |
| 5x5 |
2x5 |
|
| |
5x2 |
1x2 |
| 25 u |
10 u |
2 u |
The number of buttons that Riordan had at first is repeated. Make the number of buttons that Riordan had at first the same. LCM of 2 and 5 is 10.
| |
Eric |
Riordan |
Japheth |
| Before |
25 u |
10 u |
2 u |
| Change |
- 140 |
|
+ 140 |
| After |
5 u |
10 u |
2 u + 140 |
Number of buttons that Eric had in the end
= 10 u ÷ 2
= 5 u
Number of buttons that Eric sold to Japheth
= 25 u - 5 u
= 20 u
20 u = 140
1 u = 140 ÷ 20 = 7
Number of buttons that Japheth had in the end
= 2 u + 140
= 2 x 7 + 140
= 14 + 140
= 154
Answer(s): 154
