Linda had 45 as many coins as Ivory. The sum of the number of coins Linda and Ivory had was the same as the number of coins that Rachel had. After trading, Rachel gave 20% of her coins to Linda and received 10% of Ivory's coins. After that, Ivory 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 Linda's and Rachel's coins in the end.
| |
Linda |
Rachel |
Ivory |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
5.8 u |
7.7 u |
4.5 u |
|
| Change 3 |
- 1.35 u |
+ 1.35 u |
|
| After 2 |
12.15 u |
5.85 u |
18 u |
Total number of coins that Linda and Ivory had at first
= 4 u + 5 u
= 9 u
Number of coins that Rachel had at first = 9 u
Number of coins that Rachel gave to Linda
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of coins that Rachel received from Ivory
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of coins that Ivory increased by when she continued to trade
= 30% x 4.5 u
=
30100 x 4.5 u
= 1.35 u
Number of coins that Linda and Rachel had in the end
= 5.8 u + 7.7 u - 1.35 u
= 12.15 u
In the end
Ivory : Linda and Rachel
5.85 : 12.15
585 : 1215
13 : 27
Answer(s): 13 : 27
