Ken and Ethan had some erasers in the ratio of 4 : 3. Ethan and Valen had some erasers in the ratio of 6 : 5. Ken sold 55 erasers to Valen and ended up with half the number of erasers Ethan had. How many erasers did Valen have in the end?
| Ken |
Ethan |
Valen |
| 4x2 |
3x2 |
|
| |
6x1 |
5x1 |
| 8 u |
6 u |
5 u |
The number of erasers that Ethan had at first is repeated. Make the number of erasers that Ethan had at first the same. LCM of 3 and 6 is 6.
| |
Ken |
Ethan |
Valen |
| Before |
8 u |
6 u |
5 u |
| Change |
- 55 |
|
+ 55 |
| After |
3 u |
6 u |
5 u + 55 |
Number of erasers that Ken had in the end
= 6 u ÷ 2
= 3 u
Number of erasers that Ken sold to Valen
= 8 u - 3 u
= 5 u
5 u = 55
1 u = 55 ÷ 5 = 11
Number of erasers that Valen had in the end
= 5 u + 55
= 5 x 11 + 55
= 55 + 55
= 110
Answer(s): 110
