The ratio of the amount of money Julie had to the amount of money Xuan had was 7 : 8. Julie then gave
67 of her money to Xuan. In the end, Xuan returned $78 to Julie and they both had the same amount of money. How much money did each girl have at the beginning?
- Xuan
- Julie
|
Julie |
Xuan |
Total |
Before |
7 u |
8 u |
15 u |
Change 1 |
- 6 u |
+ 6 u |
|
After 1 |
1 u |
14 u |
15 u |
Change 2 |
+ 78 |
- 78 |
|
After 2 |
1 u + 78 |
14 u - 78 |
|
Amount that Julie and Xuan each had in the end is the same.
14 u - 78 = 1 u + 78
14 u - 1 u = 78 + 78
13 u = 156
1 u = 156 ÷ 13 = 12
Amount that Julie had at first
= 7 u
= 7 x 12
= $84
(b)
Amount that Xuan had at first
= 8 u
= 8 x 12
= $96
Answer(s): (a) $84; (b) $96