Abi had 35 as many marbles as Vanessa. The sum of the number of marbles Abi and Vanessa had was the same as the number of marbles that Tammy had. After trading, Tammy gave 10% of her marbles to Abi and received 40% of Vanessa's marbles. After that, Vanessa continued to trade and increased her number of marbles in the end by 20%, find the ratio of her number of marbles to the sum of Abi's and Tammy's marbles in the end.
| |
Abi |
Tammy |
Vanessa |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
3.8 u |
9.2 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
12.4 u |
3.6 u |
16 u |
Total number of marbles that Abi and Vanessa had at first
= 3 u + 5 u
= 8 u
Number of marbles that Tammy had at first = 8 u
Number of marbles that Tammy gave to Abi
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of marbles that Tammy received from Vanessa
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of marbles that Vanessa increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of marbles that Abi and Tammy had in the end
= 3.8 u + 9.2 u - 0.6 u
= 12.4 u
In the end
Vanessa : Abi and Tammy
3.6 : 12.4
360 : 1240
9 : 31
Answer(s): 9 : 31
