Sabrina had 45 as many beads as Hilda. The sum of the number of beads Sabrina and Hilda had was the same as the number of beads that Hazel had. After trading, Hazel gave 20% of her beads to Sabrina and received 10% of Hilda's beads. After that, Hilda continued to trade and increased her number of beads in the end by 30%, find the ratio of her number of beads to the sum of Sabrina's and Hazel's beads in the end.
| |
Sabrina |
Hazel |
Hilda |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
5.8 u |
7.7 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 beads that Sabrina and Hilda had at first
= 4 u + 5 u
= 9 u
Number of beads that Hazel had at first = 9 u
Number of beads that Hazel gave to Sabrina
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of beads that Hazel received from Hilda
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of beads that Hilda increased by when she continued to trade
= 30% x 4.5 u
=
30100 x 4.5 u
= 1.35 u
Number of beads that Sabrina and Hazel had in the end
= 5.8 u + 7.7 u - 1.35 u
= 12.15 u
In the end
Hilda : Sabrina and Hazel
5.85 : 12.15
585 : 1215
13 : 27
Answer(s): 13 : 27
