The ratio of the amount of money Diana had to the amount of money Rachel had was 4 : 5. Diana then gave
34 of her money to Rachel. In the end, Rachel returned $70 to Diana and they both had the same amount of money. How much money did each girl have at the beginning?
- Rachel
- Diana
|
Diana |
Rachel |
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 Diana and Rachel 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 Diana had at first
= 4 u
= 4 x 20
= $80
(b)
Amount that Rachel had at first
= 5 u
= 5 x 20
= $100
Answer(s): (a) $80; (b) $100