Linda had 45 as many beads as Tammy. The sum of the number of beads Linda and Tammy had was the same as the number of beads that Winnie had. After trading, Winnie gave 20% of her beads to Linda and received 20% of Tammy's beads. After that, Tammy continued to trade and increased her number of beads in the end by 30%, find the ratio of her number of beads to the sum of Linda's and Winnie's beads in the end.
| |
Linda |
Winnie |
Tammy |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
5.8 u |
8.2 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
12.8 u |
5.2 u |
18 u |
Total number of beads that Linda and Tammy had at first
= 4 u + 5 u
= 9 u
Number of beads that Winnie had at first = 9 u
Number of beads that Winnie gave to Linda
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of beads that Winnie received from Tammy
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of beads that Tammy increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of beads that Linda and Winnie had in the end
= 5.8 u + 8.2 u - 1.2 u
= 12.8 u
In the end
Tammy : Linda and Winnie
5.2 : 12.8
520 : 1280
13 : 32
Answer(s): 13 : 32
