Tiffany had 35 as many beads as Abi. The sum of the number of beads Tiffany and Abi had was the same as the number of beads that Dana had. After trading, Dana gave 20% of her beads to Tiffany and received 40% of Abi's beads. After that, Abi continued to trade and increased her number of beads in the end by 20%, find the ratio of her number of beads to the sum of Tiffany's and Dana's beads in the end.
| |
Tiffany |
Dana |
Abi |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 1.6 u |
- 1.6 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
4.6 u |
8.4 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
12.4 u |
3.6 u |
16 u |
Total number of beads that Tiffany and Abi had at first
= 3 u + 5 u
= 8 u
Number of beads that Dana had at first = 8 u
Number of beads that Dana gave to Tiffany
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of beads that Dana received from Abi
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of beads that Abi increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of beads that Tiffany and Dana had in the end
= 4.6 u + 8.4 u - 0.6 u
= 12.4 u
In the end
Abi : Tiffany and Dana
3.6 : 12.4
360 : 1240
9 : 31
Answer(s): 9 : 31
