Lynn had 45 as many beads as Barbara. The sum of the number of beads Lynn and Barbara had was the same as the number of beads that Gabby had. After trading, Gabby gave 20% of her beads to Lynn and received 10% of Barbara's beads. After that, Barbara 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 Lynn's and Gabby's beads in the end.
| |
Lynn |
Gabby |
Barbara |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
5.8 u |
7.7 u |
4.5 u |
|
| Change 3 |
- 0.9 u |
+ 0.9 u |
|
| After 2 |
12.6 u |
5.4 u |
18 u |
Total number of beads that Lynn and Barbara had at first
= 4 u + 5 u
= 9 u
Number of beads that Gabby had at first = 9 u
Number of beads that Gabby gave to Lynn
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of beads that Gabby received from Barbara
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of beads that Barbara increased by when she continued to trade
= 20% x 4.5 u
=
20100 x 4.5 u
= 0.9 u
Number of beads that Lynn and Gabby had in the end
= 5.8 u + 7.7 u - 0.9 u
= 12.6 u
In the end
Barbara : Lynn and Gabby
5.4 : 12.6
540 : 1260
3 : 7
Answer(s): 3 : 7
