Elyse had 35 as many beads as Kathy. The sum of the number of beads Elyse and Kathy had was the same as the number of beads that Abi had. After trading, Abi gave 20% of her beads to Elyse and received 20% of Kathy's beads. After that, Kathy continued to trade and increased her number of beads in the end by 10%, find the ratio of her number of beads to the sum of Elyse's and Abi's beads in the end.
| |
Elyse |
Abi |
Kathy |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 1.6 u |
- 1.6 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
4.6 u |
7.4 u |
4 u |
|
| Change 3 |
- 0.4 u |
+ 0.4 u |
|
| After 2 |
11.6 u |
4.4 u |
16 u |
Total number of beads that Elyse and Kathy had at first
= 3 u + 5 u
= 8 u
Number of beads that Abi had at first = 8 u
Number of beads that Abi gave to Elyse
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of beads that Abi received from Kathy
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of beads that Kathy increased by when she continued to trade
= 10% x 4 u
=
10100 x 4 u
= 0.4 u
Number of beads that Elyse and Abi had in the end
= 4.6 u + 7.4 u - 0.4 u
= 11.6 u
In the end
Kathy : Elyse and Abi
4.4 : 11.6
440 : 1160
11 : 29
Answer(s): 11 : 29
