Howard and Asher had some beads in the ratio of 6 : 5. Asher and Paul had some beads in the ratio of 10 : 7. Howard sold 42 beads to Paul and ended up with half the number of beads Asher had. How many beads did Paul have in the end?
| Howard |
Asher |
Paul |
| 6x2 |
5x2 |
|
| |
10x1 |
7x1 |
| 12 u |
10 u |
7 u |
The number of beads that Asher had at first is repeated. Make the number of beads that Asher had at first the same. LCM of 5 and 10 is 10.
| |
Howard |
Asher |
Paul |
| Before |
12 u |
10 u |
7 u |
| Change |
- 42 |
|
+ 42 |
| After |
5 u |
10 u |
7 u + 42 |
Number of beads that Howard had in the end
= 10 u ÷ 2
= 5 u
Number of beads that Howard sold to Paul
= 12 u - 5 u
= 7 u
7 u = 42
1 u = 42 ÷ 7 = 6
Number of beads that Paul had in the end
= 7 u + 42
= 7 x 6 + 42
= 42 + 42
= 84
Answer(s): 84
