Abi had 45 as many coins as Cindy. The sum of the number of coins Abi and Cindy had was the same as the number of coins that Linda had. After trading, Linda gave 20% of her coins to Abi and received 30% of Cindy's coins. After that, Cindy continued to trade and increased her number of coins in the end by 20%, find the ratio of her number of coins to the sum of Abi's and Linda's coins in the end.
| |
Abi |
Linda |
Cindy |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1.5 u |
- 1.5 u |
|
| After 1 |
5.8 u |
8.7 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 coins that Abi and Cindy had at first
= 4 u + 5 u
= 9 u
Number of coins that Linda had at first = 9 u
Number of coins that Linda gave to Abi
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of coins that Linda received from Cindy
= 30% x 5 u
=
30100 x 5 u
= 1.5 u
Number of coins that Cindy increased by when she continued to trade
= 20% x 3.5 u
=
20100 x 3.5 u
= 0.7 u
Number of coins that Abi and Linda had in the end
= 5.8 u + 8.7 u - 0.7 u
= 13.8 u
In the end
Cindy : Abi and Linda
4.2 : 13.8
420 : 1380
7 : 23
Answer(s): 7 : 23
