Opal had 45 as many beads as Yen. The sum of the number of beads Opal and Yen had was the same as the number of beads that Ivory had. After trading, Ivory gave 30% of her beads to Opal and received 30% of Yen's beads. After that, Yen 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 Opal's and Ivory's beads in the end.
| |
Opal |
Ivory |
Yen |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 1.5 u |
- 1.5 u |
|
| After 1 |
6.7 u |
7.8 u |
3.5 u |
|
| Change 3 |
- 0.7 u |
+ 0.7 u |
|
| After 2 |
13.8 u |
4.2 u |
18 u |
Total number of beads that Opal and Yen had at first
= 4 u + 5 u
= 9 u
Number of beads that Ivory had at first = 9 u
Number of beads that Ivory gave to Opal
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of beads that Ivory received from Yen
= 30% x 5 u
=
30100 x 5 u
= 1.5 u
Number of beads that Yen increased by when she continued to trade
= 20% x 3.5 u
=
20100 x 3.5 u
= 0.7 u
Number of beads that Opal and Ivory had in the end
= 6.7 u + 7.8 u - 0.7 u
= 13.8 u
In the end
Yen : Opal and Ivory
4.2 : 13.8
420 : 1380
7 : 23
Answer(s): 7 : 23
