Billy, Peter and Archie have some beads. The ratios of their beads are as follows:
Billy : (Billy + Peter + Archie) = 2 : 5
Peter : (Billy + Archie) = 1 : 3
Archie has 14 beads more than Peter. In the end, Archie gives away all he has to Peter and Billy so that both Peter and Billy end up with the same number of beads, how many beads has Billy received from Archie?
Peter |
Archie |
Billy |
Total |
3x4 |
2x4 |
5x4 |
1x5 |
3x5 |
4x5 |
5 u |
7 u |
8 u |
20 u |
The total number of beads is repeated. Make the total number of beads the same. LCM of 5 and 4 is 20.
Number of beads that Archie has more than Peter
= 7 u - 5 u
= 2 u
2 u = 14
1 u = 14 ÷ 2 = 7
|
Peter |
Archie |
Billy |
Before |
5 u |
7 u |
8 u |
Change |
+ 5 u |
- 7 u |
+ 2 u |
After |
10 u |
0 u |
10 u |
Number of beads that Billy has received from Archie
= 10 u - 8 u
= 2 u
= 2 x 7
= 14
Answer(s): 14