Natalie had 35 as many beads as Betty. The sum of the number of beads Natalie and Betty had was the same as the number of beads that Mary had. After trading, Mary gave 30% of her beads to Natalie and received 20% of Betty's beads. After that, Betty 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 Natalie's and Mary's beads in the end.
| |
Natalie |
Mary |
Betty |
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 |
- 0.8 u |
+ 0.8 u |
|
| After 2 |
11.2 u |
4.8 u |
16 u |
Total number of beads that Natalie and Betty had at first
= 3 u + 5 u
= 8 u
Number of beads that Mary had at first = 8 u
Number of beads that Mary gave to Natalie
= 30% x 8 u
=
30100 x 3 u
= 2.4 u
Number of beads that Mary received from Betty
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of beads that Betty increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of beads that Natalie and Mary had in the end
= 5.4 u + 6.6 u - 0.8 u
= 11.2 u
In the end
Betty : Natalie and Mary
4.8 : 11.2
480 : 1120
3 : 7
Answer(s): 3 : 7
