The ratio of the amount of money Shiyun had to the amount of money Zara had was 4 : 5. Shiyun then gave
34 of her money to Zara. In the end, Zara returned $70 to Shiyun and they both had the same amount of money. How much money did each girl have at the beginning?
- Zara
- Shiyun
|
Shiyun |
Zara |
Total |
Before |
4 u |
5 u |
9 u |
Change 1 |
- 3 u |
+ 3 u |
|
After 1 |
1 u |
8 u |
9 u |
Change 2 |
+ 70 |
- 70 |
|
After 2 |
1 u + 70 |
8 u - 70 |
|
Amount that Shiyun and Zara each had in the end is the same.
8 u - 70 = 1 u + 70
8 u - 1 u = 70 + 70
7 u = 140
1 u = 140 ÷ 7 = 20
Amount that Shiyun had at first
= 4 u
= 4 x 20
= $80
(b)
Amount that Zara had at first
= 5 u
= 5 x 20
= $100
Answer(s): (a) $80; (b) $100