Jean had 45 as many buttons as Betty. The sum of the number of buttons Jean and Betty had was the same as the number of buttons that Tammy had. After trading, Tammy gave 20% of her buttons to Jean and received 40% of Betty's buttons. After that, Betty continued to trade and increased her number of buttons in the end by 10%, find the ratio of her number of buttons to the sum of Jean's and Tammy's buttons in the end.
| |
Jean |
Tammy |
Betty |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
5.8 u |
9.2 u |
3 u |
|
| Change 3 |
- 0.3 u |
+ 0.3 u |
|
| After 2 |
14.7 u |
3.3 u |
18 u |
Total number of buttons that Jean and Betty had at first
= 4 u + 5 u
= 9 u
Number of buttons that Tammy had at first = 9 u
Number of buttons that Tammy gave to Jean
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of buttons that Tammy received from Betty
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of buttons that Betty increased by when she continued to trade
= 10% x 3 u
=
10100 x 3 u
= 0.3 u
Number of buttons that Jean and Tammy had in the end
= 5.8 u + 9.2 u - 0.3 u
= 14.7 u
In the end
Betty : Jean and Tammy
3.3 : 14.7
330 : 1470
11 : 49
Answer(s): 11 : 49
