Ben, Gabriel and Peter have some beads. The ratios of their beads are as follows:
Ben : (Ben + Gabriel + Peter) = 1 : 5
Gabriel : (Ben + Peter) = 1 : 3
Peter has 12 beads more than Gabriel. In the end, Peter gives away all he has to Gabriel and Ben so that both Gabriel and Ben end up with the same number of beads, how many beads has Gabriel received from Peter?
Gabriel |
Peter |
Ben |
Total |
4x4 |
1x4 |
5x4 |
1x5 |
3x5 |
4x5 |
5 u |
11 u |
4 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 Peter has more than Gabriel
= 11 u - 5 u
= 6 u
6 u = 12
1 u = 12 ÷ 6 = 2
|
Gabriel |
Peter |
Ben |
Before |
5 u |
11 u |
4 u |
Change |
+ 5 u |
- 11 u |
+ 6 u |
After |
10 u |
0 u |
10 u |
Number of beads that Gabriel has received from Peter
= 10 u - 5 u
= 5 u
= 5 x 2
= 10
Answer(s): 10