The ratio of the amount of money Dana had to the amount of money Xuan had was 4 : 5. Dana then gave
34 of her money to Xuan. In the end, Xuan returned $56 to Dana and they both had the same amount of money. How much money did each girl have at the beginning?
- Xuan
- Dana
|
Dana |
Xuan |
Total |
Before |
4 u |
5 u |
9 u |
Change 1 |
- 3 u |
+ 3 u |
|
After 1 |
1 u |
8 u |
9 u |
Change 2 |
+ 56 |
- 56 |
|
After 2 |
1 u + 56 |
8 u - 56 |
|
Amount that Dana and Xuan each had in the end is the same.
8 u - 56 = 1 u + 56
8 u - 1 u = 56 + 56
7 u = 112
1 u = 112 ÷ 7 = 16
Amount that Dana had at first
= 4 u
= 4 x 16
= $64
(b)
Amount that Xuan had at first
= 5 u
= 5 x 16
= $80
Answer(s): (a) $64; (b) $80