Zara had 45 as many stamps as Natalie. The sum of the number of stamps Zara and Natalie had was the same as the number of stamps that Wendy had. After trading, Wendy gave 10% of her stamps to Zara and received 10% of Natalie's stamps. After that, Natalie continued to trade and increased her number of stamps in the end by 30%, find the ratio of her number of stamps to the sum of Zara's and Wendy's stamps in the end.
| |
Zara |
Wendy |
Natalie |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
4.9 u |
8.6 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 stamps that Zara and Natalie had at first
= 4 u + 5 u
= 9 u
Number of stamps that Wendy had at first = 9 u
Number of stamps that Wendy gave to Zara
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of stamps that Wendy received from Natalie
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of stamps that Natalie increased by when she continued to trade
= 30% x 4.5 u
=
30100 x 4.5 u
= 1.35 u
Number of stamps that Zara and Wendy had in the end
= 4.9 u + 8.6 u - 1.35 u
= 12.15 u
In the end
Natalie : Zara and Wendy
5.85 : 12.15
585 : 1215
13 : 27
Answer(s): 13 : 27
