Gwen had 45 as many beads as Lynn. The sum of the number of beads Gwen and Lynn had was the same as the number of beads that Yen had. After trading, Yen gave 30% of her beads to Gwen and received 30% of Lynn's beads. After that, Lynn 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 Gwen's and Yen's beads in the end.
| |
Gwen |
Yen |
Lynn |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 1.5 u |
- 1.5 u |
|
| After 1 |
6.7 u |
7.8 u |
3.5 u |
|
| Change 3 |
- 0.7 u |
+ 0.7 u |
|
| After 2 |
13.8 u |
4.2 u |
18 u |
Total number of beads that Gwen and Lynn had at first
= 4 u + 5 u
= 9 u
Number of beads that Yen had at first = 9 u
Number of beads that Yen gave to Gwen
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of beads that Yen received from Lynn
= 30% x 5 u
=
30100 x 5 u
= 1.5 u
Number of beads that Lynn increased by when she continued to trade
= 20% x 3.5 u
=
20100 x 3.5 u
= 0.7 u
Number of beads that Gwen and Yen had in the end
= 6.7 u + 7.8 u - 0.7 u
= 13.8 u
In the end
Lynn : Gwen and Yen
4.2 : 13.8
420 : 1380
7 : 23
Answer(s): 7 : 23
