Jenson and Bryan had some erasers in the ratio of 9 : 8. Bryan and Nick had some erasers in the ratio of 3 : 2. Jenson sold 105 erasers to Nick and ended up with half the number of erasers Bryan had. How many erasers did Nick have in the end?
| Jenson |
Bryan |
Nick |
| 9x3 |
8x3 |
|
| |
3x8 |
2x8 |
| 27 u |
24 u |
16 u |
The number of erasers that Bryan had at first is repeated. Make the number of erasers that Bryan had at first the same. LCM of 8 and 3 is 24.
| |
Jenson |
Bryan |
Nick |
| Before |
27 u |
24 u |
16 u |
| Change |
- 105 |
|
+ 105 |
| After |
12 u |
24 u |
16 u + 105 |
Number of erasers that Jenson had in the end
= 24 u ÷ 2
= 12 u
Number of erasers that Jenson sold to Nick
= 27 u - 12 u
= 15 u
15 u = 105
1 u = 105 ÷ 15 = 7
Number of erasers that Nick had in the end
= 16 u + 105
= 16 x 7 + 105
= 112 + 105
= 217
Answer(s): 217
