Shannon, Xylia and Emma had a sum of money. The amount of money Shannon had was
34 of the amount of money Xylia had. The ratio of the amount of money Xylia had to the total amount of money Emma and Xylia had was 3: 7. After Emma gave $80 to Xylia, she had as much money as Xylia. How much more money did Emma have than Shannon in the end?
Shannon |
Xylia |
Emma |
3x3 = 9 u |
4x3 = 12 u |
|
|
3x4 = 12 u |
4x4 = 16 u |
9 u |
12 u |
16 u |
The amount that Xylia had is the repeated identity. Make the amount that Xylia had the same. LCM of 4 and 3 is 12.
|
Shannon |
Xylia |
Emma |
Before |
9 u |
12 u |
16 u |
Change |
No change |
+ 80 |
- 80 |
After |
9 u |
12 u + 80 |
16 u - 80 |
The amount that Emma and Xylia had in the end is the same.
16 u - 80 = 12 u + 80
16 u - 12 u = 80 + 80
4 u = 160
1 u = 160 ÷ 4 = 40
Amount that Emma had more than Shannon in the end
= 16 u - 80 - 9 u
= 7 u - 80
= 7 x 40 - 80
= 280 - 80
= $200
Answer(s): $200