Tammy had 35 as many erasers as Usha. The sum of the number of erasers Tammy and Usha had was the same as the number of erasers that Elyse had. After trading, Elyse gave 20% of her erasers to Tammy and received 40% of Usha's erasers. After that, Usha continued to trade and increased her number of erasers in the end by 20%, find the ratio of her number of erasers to the sum of Tammy's and Elyse's erasers in the end.
| |
Tammy |
Elyse |
Usha |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 1.6 u |
- 1.6 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
4.6 u |
8.4 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
12.4 u |
3.6 u |
16 u |
Total number of erasers that Tammy and Usha had at first
= 3 u + 5 u
= 8 u
Number of erasers that Elyse had at first = 8 u
Number of erasers that Elyse gave to Tammy
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of erasers that Elyse received from Usha
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of erasers that Usha increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of erasers that Tammy and Elyse had in the end
= 4.6 u + 8.4 u - 0.6 u
= 12.4 u
In the end
Usha : Tammy and Elyse
3.6 : 12.4
360 : 1240
9 : 31
Answer(s): 9 : 31
