Kimberly had 45 as many beads as Linda. The sum of the number of beads Kimberly and Linda had was the same as the number of beads that Marion had. After trading, Marion gave 20% of her beads to Kimberly and received 40% of Linda's beads. After that, Linda continued to trade and increased her number of beads in the end by 20%, find the ratio of her number of beads to the sum of Kimberly's and Marion's beads in the end.
| |
Kimberly |
Marion |
Linda |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
5.8 u |
9.2 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
14.4 u |
3.6 u |
18 u |
Total number of beads that Kimberly and Linda had at first
= 4 u + 5 u
= 9 u
Number of beads that Marion had at first = 9 u
Number of beads that Marion gave to Kimberly
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of beads that Marion received from Linda
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of beads that Linda increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of beads that Kimberly and Marion had in the end
= 5.8 u + 9.2 u - 0.6 u
= 14.4 u
In the end
Linda : Kimberly and Marion
3.6 : 14.4
360 : 1440
1 : 4
Answer(s): 1 : 4
