Abi had 45 as many buttons as Tammy. The sum of the number of buttons Abi and Tammy had was the same as the number of buttons that Lucy had. After trading, Lucy gave 10% of her buttons to Abi and received 25% of Tammy's buttons. After that, Tammy continued to trade and increased her number of buttons in the end by 20%, find the ratio of her number of buttons to the sum of Abi's and Lucy's buttons in the end.
| |
Abi |
Lucy |
Tammy |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
4.9 u |
9.35 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
13.5 u |
4.5 u |
18 u |
Total number of buttons that Abi and Tammy had at first
= 4 u + 5 u
= 9 u
Number of buttons that Lucy had at first = 9 u
Number of buttons that Lucy gave to Abi
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of buttons that Lucy received from Tammy
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of buttons that Tammy increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of buttons that Abi and Lucy had in the end
= 4.9 u + 9.35 u - 0.75 u
= 13.5 u
In the end
Tammy : Abi and Lucy
4.5 : 13.5
450 : 1350
1 : 3
Answer(s): 1 : 3
