The ratio of the amount of money Xuan had to the amount of money Betty had was 6 : 7. Xuan then gave
56 of her money to Betty. In the end, Betty returned $44 to Xuan and they both had the same amount of money. How much money did each girl have at the beginning?
- Betty
- Xuan
|
Xuan |
Betty |
Total |
Before |
6 u |
7 u |
13 u |
Change 1 |
- 5 u |
+ 5 u |
|
After 1 |
1 u |
12 u |
13 u |
Change 2 |
+ 44 |
- 44 |
|
After 2 |
1 u + 44 |
12 u - 44 |
|
Amount that Xuan and Betty each had in the end is the same.
12 u - 44 = 1 u + 44
12 u - 1 u = 44 + 44
11 u = 88
1 u = 88 ÷ 11 = 8
Amount that Xuan had at first
= 6 u
= 6 x 8
= $48
(b)
Amount that Betty had at first
= 7 u
= 7 x 8
= $56
Answer(s): (a) $48; (b) $56