Tina, Emma and Hilda had a sum of money. The amount of money Tina had was
35 of the amount of money Emma had. The ratio of the amount of money Emma had to the total amount of money Hilda and Emma had was 2: 5. After Hilda gave $30 to Emma, she had as much money as Emma. How much more money did Hilda have than Tina in the end?
Tina |
Emma |
Hilda |
3x2 = 6 u |
5x2 = 10 u |
|
|
2x5 = 10 u |
3x5 = 15 u |
6 u |
10 u |
15 u |
The amount that Emma had is the repeated identity. Make the amount that Emma had the same. LCM of 5 and 2 is 10.
|
Tina |
Emma |
Hilda |
Before |
6 u |
10 u |
15 u |
Change |
No change |
+ 30 |
- 30 |
After |
6 u |
10 u + 30 |
15 u - 30 |
The amount that Hilda and Emma had in the end is the same.
15 u - 30 = 10 u + 30
15 u - 10 u = 30 + 30
5 u = 60
1 u = 60 ÷ 5 = 12
Amount that Hilda had more than Tina in the end
= 15 u - 30 - 6 u
= 9 u - 30
= 9 x 12 - 30
= 108 - 30
= $78
Answer(s): $78