Seth and Ethan had some erasers in the ratio of 5 : 2. Ethan and Bryan had some erasers in the ratio of 9 : 2. Seth sold 180 erasers to Bryan and ended up with half the number of erasers Ethan had. How many erasers did Bryan have in the end?
| Seth |
Ethan |
Bryan |
| 5x9 |
2x9 |
|
| |
9x2 |
2x2 |
| 45 u |
18 u |
4 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 2 and 9 is 18.
| |
Seth |
Ethan |
Bryan |
| Before |
45 u |
18 u |
4 u |
| Change |
- 180 |
|
+ 180 |
| After |
9 u |
18 u |
4 u + 180 |
Number of erasers that Seth had in the end
= 18 u ÷ 2
= 9 u
Number of erasers that Seth sold to Bryan
= 45 u - 9 u
= 36 u
36 u = 180
1 u = 180 ÷ 36 = 5
Number of erasers that Bryan had in the end
= 4 u + 180
= 4 x 5 + 180
= 20 + 180
= 200
Answer(s): 200
