Nick and Zane had some beads in the ratio of 5 : 2. Zane and Owen had some beads in the ratio of 3 : 2. Nick sold 84 beads to Owen and ended up with half the number of beads Zane had. How many beads did Owen have in the end?
| Nick |
Zane |
Owen |
| 5x3 |
2x3 |
|
| |
3x2 |
2x2 |
| 15 u |
6 u |
4 u |
The number of beads that Zane had at first is repeated. Make the number of beads that Zane had at first the same. LCM of 2 and 3 is 6.
| |
Nick |
Zane |
Owen |
| Before |
15 u |
6 u |
4 u |
| Change |
- 84 |
|
+ 84 |
| After |
3 u |
6 u |
4 u + 84 |
Number of beads that Nick had in the end
= 6 u ÷ 2
= 3 u
Number of beads that Nick sold to Owen
= 15 u - 3 u
= 12 u
12 u = 84
1 u = 84 ÷ 12 = 7
Number of beads that Owen had in the end
= 4 u + 84
= 4 x 7 + 84
= 28 + 84
= 112
Answer(s): 112
