Sabrina, Kathy and Natalie had a sum of money. The amount of money Sabrina had was
45 of the amount of money Kathy had. The ratio of the amount of money Kathy had to the total amount of money Natalie and Kathy had was 3: 7. After Natalie gave $100 to Kathy, she had as much money as Kathy. How much more money did Natalie have than Sabrina in the end?
Sabrina |
Kathy |
Natalie |
4x3 = 12 u |
5x3 = 15 u |
|
|
3x5 = 15 u |
4x5 = 20 u |
12 u |
15 u |
20 u |
The amount that Kathy had is the repeated identity. Make the amount that Kathy had the same. LCM of 5 and 3 is 15.
|
Sabrina |
Kathy |
Natalie |
Before |
12 u |
15 u |
20 u |
Change |
No change |
+ 100 |
- 100 |
After |
12 u |
15 u + 100 |
20 u - 100 |
The amount that Natalie and Kathy had in the end is the same.
20 u - 100 = 15 u + 100
20 u - 15 u = 100 + 100
5 u = 200
1 u = 200 ÷ 5 = 40
Amount that Natalie had more than Sabrina in the end
= 20 u - 100 - 12 u
= 8 u - 100
= 8 x 40 - 100
= 320 - 100
= $220
Answer(s): $220