Elyse had 45 as many coins as Jean. The sum of the number of coins Elyse and Jean had was the same as the number of coins that Sarah had. After trading, Sarah gave 30% of her coins to Elyse and received 20% of Jean's coins. After that, Jean continued to trade and increased her number of coins in the end by 30%, find the ratio of her number of coins to the sum of Elyse's and Sarah's coins in the end.
| |
Elyse |
Sarah |
Jean |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
6.7 u |
7.3 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
12.8 u |
5.2 u |
18 u |
Total number of coins that Elyse and Jean had at first
= 4 u + 5 u
= 9 u
Number of coins that Sarah had at first = 9 u
Number of coins that Sarah gave to Elyse
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of coins that Sarah received from Jean
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of coins that Jean increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of coins that Elyse and Sarah had in the end
= 6.7 u + 7.3 u - 1.2 u
= 12.8 u
In the end
Jean : Elyse and Sarah
5.2 : 12.8
520 : 1280
13 : 32
Answer(s): 13 : 32
