The ratio of the amount of money Emma had to the amount of money Diana had was 4 : 5. Emma then gave
34 of her money to Diana. In the end, Diana returned $63 to Emma and they both had the same amount of money. How much money did each girl have at the beginning?
- Diana
- Emma
|
Emma |
Diana |
Total |
Before |
4 u |
5 u |
9 u |
Change 1 |
- 3 u |
+ 3 u |
|
After 1 |
1 u |
8 u |
9 u |
Change 2 |
+ 63 |
- 63 |
|
After 2 |
1 u + 63 |
8 u - 63 |
|
Amount that Emma and Diana each had in the end is the same.
8 u - 63 = 1 u + 63
8 u - 1 u = 63 + 63
7 u = 126
1 u = 126 ÷ 7 = 18
Amount that Emma had at first
= 4 u
= 4 x 18
= $72
(b)
Amount that Diana had at first
= 5 u
= 5 x 18
= $90
Answer(s): (a) $72; (b) $90