Risa, Xylia and Esther had a sum of money. The amount of money Risa had was
45 of the amount of money Xylia had. The ratio of the amount of money Xylia had to the total amount of money Esther and Xylia had was 4: 9. After Esther gave $100 to Xylia, she had as much money as Xylia. How much more money did Esther have than Risa in the end?
Risa |
Xylia |
Esther |
4x4 = 16 u |
5x4 = 20 u |
|
|
4x5 = 20 u |
5x5 = 25 u |
16 u |
20 u |
25 u |
The amount that Xylia had is the repeated identity. Make the amount that Xylia had the same. LCM of 5 and 4 is 20.
|
Risa |
Xylia |
Esther |
Before |
16 u |
20 u |
25 u |
Change |
No change |
+ 100 |
- 100 |
After |
16 u |
20 u + 100 |
25 u - 100 |
The amount that Esther and Xylia had in the end is the same.
25 u - 100 = 20 u + 100
25 u - 20 u = 100 + 100
5 u = 200
1 u = 200 ÷ 5 = 40
Amount that Esther had more than Risa in the end
= 25 u - 100 - 16 u
= 9 u - 100
= 9 x 40 - 100
= 360 - 100
= $260
Answer(s): $260