Xylia had 45 as many beads as Barbara. The sum of the number of beads Xylia and Barbara had was the same as the number of beads that Mary had. After trading, Mary gave 10% of her beads to Xylia and received 20% 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 Xylia's and Mary's beads in the end.
| |
Xylia |
Mary |
Barbara |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
4.9 u |
9.1 u |
4 u |
|
| Change 3 |
- 0.8 u |
+ 0.8 u |
|
| After 2 |
13.2 u |
4.8 u |
18 u |
Total number of beads that Xylia and Barbara had at first
= 4 u + 5 u
= 9 u
Number of beads that Mary had at first = 9 u
Number of beads that Mary gave to Xylia
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of beads that Mary received from Barbara
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of beads that Barbara increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of beads that Xylia and Mary had in the end
= 4.9 u + 9.1 u - 0.8 u
= 13.2 u
In the end
Barbara : Xylia and Mary
4.8 : 13.2
480 : 1320
4 : 11
Answer(s): 4 : 11
