The ratio of the amount of money Hazel had to the amount of money Xuan had was 5 : 6. Hazel then gave
45 of her money to Xuan. In the end, Xuan returned $54 to Hazel and they both had the same amount of money. How much money did each girl have at the beginning?
- Xuan
- Hazel
|
Hazel |
Xuan |
Total |
Before |
5 u |
6 u |
11 u |
Change 1 |
- 4 u |
+ 4 u |
|
After 1 |
1 u |
10 u |
11 u |
Change 2 |
+ 54 |
- 54 |
|
After 2 |
1 u + 54 |
10 u - 54 |
|
Amount that Hazel and Xuan each had in the end is the same.
10 u - 54 = 1 u + 54
10 u - 1 u = 54 + 54
9 u = 108
1 u = 108 ÷ 9 = 12
Amount that Hazel had at first
= 5 u
= 5 x 12
= $60
(b)
Amount that Xuan had at first
= 6 u
= 6 x 12
= $72
Answer(s): (a) $60; (b) $72