Yen had 45 as many beads as Barbara. The sum of the number of beads Yen and Barbara had was the same as the number of beads that Sabrina had. After trading, Sabrina gave 10% of her beads to Yen and received 30% 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 Yen's and Sabrina's beads in the end.
| |
Yen |
Sabrina |
Barbara |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1.5 u |
- 1.5 u |
|
| After 1 |
4.9 u |
9.6 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 Yen and Barbara had at first
= 4 u + 5 u
= 9 u
Number of beads that Sabrina had at first = 9 u
Number of beads that Sabrina gave to Yen
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of beads that Sabrina received from Barbara
= 30% x 5 u
=
30100 x 5 u
= 1.5 u
Number of beads that Barbara increased by when she continued to trade
= 20% x 3.5 u
=
20100 x 3.5 u
= 0.7 u
Number of beads that Yen and Sabrina had in the end
= 4.9 u + 9.6 u - 0.7 u
= 13.8 u
In the end
Barbara : Yen and Sabrina
4.2 : 13.8
420 : 1380
7 : 23
Answer(s): 7 : 23
