Gillian had 45 as many marbles as Zara. The sum of the number of marbles Gillian and Zara had was the same as the number of marbles that Irene had. After trading, Irene gave 10% of her marbles to Gillian and received 25% of Zara's marbles. After that, Zara continued to trade and increased her number of marbles in the end by 20%, find the ratio of her number of marbles to the sum of Gillian's and Irene's marbles in the end.
| |
Gillian |
Irene |
Zara |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
4.9 u |
9.35 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
13.5 u |
4.5 u |
18 u |
Total number of marbles that Gillian and Zara had at first
= 4 u + 5 u
= 9 u
Number of marbles that Irene had at first = 9 u
Number of marbles that Irene gave to Gillian
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of marbles that Irene received from Zara
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of marbles that Zara increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of marbles that Gillian and Irene had in the end
= 4.9 u + 9.35 u - 0.75 u
= 13.5 u
In the end
Zara : Gillian and Irene
4.5 : 13.5
450 : 1350
1 : 3
Answer(s): 1 : 3
