Vanessa had 35 as many stickers as Rachel. The sum of the number of stickers Vanessa and Rachel had was the same as the number of stickers that Hazel had. After trading, Hazel gave 30% of her stickers to Vanessa and received 20% of Rachel's stickers. After that, Rachel continued to trade and increased her number of stickers in the end by 30%, find the ratio of her number of stickers to the sum of Vanessa's and Hazel's stickers in the end.
| |
Vanessa |
Hazel |
Rachel |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 2.4 u |
- 2.4 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
5.4 u |
6.6 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
10.8 u |
5.2 u |
16 u |
Total number of stickers that Vanessa and Rachel had at first
= 3 u + 5 u
= 8 u
Number of stickers that Hazel had at first = 8 u
Number of stickers that Hazel gave to Vanessa
= 30% x 8 u
=
30100 x 3 u
= 2.4 u
Number of stickers that Hazel received from Rachel
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of stickers that Rachel increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of stickers that Vanessa and Hazel had in the end
= 5.4 u + 6.6 u - 1.2 u
= 10.8 u
In the end
Rachel : Vanessa and Hazel
5.2 : 10.8
520 : 1080
13 : 27
Answer(s): 13 : 27
