Paul, Ian and Charlie have some beads. The ratios of their beads are as follows:
Paul : (Paul + Ian + Charlie) = 2 : 5
Ian : (Paul + Charlie) = 1 : 3
Charlie has 18 beads more than Ian. In the end, Charlie gives away all he has to Ian and Paul so that both Ian and Paul end up with the same number of beads, how many beads has Ian received from Charlie?
Ian |
Charlie |
Paul |
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 Charlie has more than Ian
= 7 u - 5 u
= 2 u
2 u = 18
1 u = 18 ÷ 2 = 9
|
Ian |
Charlie |
Paul |
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 Ian has received from Charlie
= 10 u - 5 u
= 5 u
= 5 x 9
= 45
Answer(s): 45