Anna had 35 as many stickers as Abi. The sum of the number of stickers Anna and Abi had was the same as the number of stickers that Cathy had. After trading, Cathy gave 30% of her stickers to Anna and received 40% of Abi's stickers. After that, Abi continued to trade and increased her number of stickers in the end by 20%, find the ratio of her number of stickers to the sum of Anna's and Cathy's stickers in the end.
| |
Anna |
Cathy |
Abi |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 2.4 u |
- 2.4 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
5.4 u |
7.6 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
12.4 u |
3.6 u |
16 u |
Total number of stickers that Anna and Abi had at first
= 3 u + 5 u
= 8 u
Number of stickers that Cathy had at first = 8 u
Number of stickers that Cathy gave to Anna
= 30% x 8 u
=
30100 x 3 u
= 2.4 u
Number of stickers that Cathy received from Abi
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of stickers that Abi increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of stickers that Anna and Cathy had in the end
= 5.4 u + 7.6 u - 0.6 u
= 12.4 u
In the end
Abi : Anna and Cathy
3.6 : 12.4
360 : 1240
9 : 31
Answer(s): 9 : 31
