Erika, Anna and Cathy had a sum of money. The amount of money Erika had was
34 of the amount of money Anna had. The ratio of the amount of money Anna had to the total amount of money Cathy and Anna had was 2: 7. After Cathy gave $57 to Anna, she had as much money as Anna. How much more money did Cathy have than Erika in the end?
Erika |
Anna |
Cathy |
3x1 = 3 u |
4x1 = 4 u |
|
|
2x2 = 4 u |
5x2 = 10 u |
3 u |
4 u |
10 u |
The amount that Anna had is the repeated identity. Make the amount that Anna had the same. LCM of 4 and 2 is 4.
|
Erika |
Anna |
Cathy |
Before |
3 u |
4 u |
10 u |
Change |
No change |
+ 57 |
- 57 |
After |
3 u |
4 u + 57 |
10 u - 57 |
The amount that Cathy and Anna had in the end is the same.
10 u - 57 = 4 u + 57
10 u - 4 u = 57 + 57
6 u = 114
1 u = 114 ÷ 6 = 19
Amount that Cathy had more than Erika in the end
= 10 u - 57 - 3 u
= 7 u - 57
= 7 x 19 - 57
= 133 - 57
= $76
Answer(s): $76