The ratio of the amount of money Emma had to the amount of money Fanny had was 5 : 6. Emma then gave
45 of her money to Fanny. In the end, Fanny returned $45 to Emma and they both had the same amount of money. How much money did each girl have at the beginning?
- Fanny
- Emma
|
Emma |
Fanny |
Total |
Before |
5 u |
6 u |
11 u |
Change 1 |
- 4 u |
+ 4 u |
|
After 1 |
1 u |
10 u |
11 u |
Change 2 |
+ 45 |
- 45 |
|
After 2 |
1 u + 45 |
10 u - 45 |
|
Amount that Emma and Fanny each had in the end is the same.
10 u - 45 = 1 u + 45
10 u - 1 u = 45 + 45
9 u = 90
1 u = 90 ÷ 9 = 10
Amount that Emma had at first
= 5 u
= 5 x 10
= $50
(b)
Amount that Fanny had at first
= 6 u
= 6 x 10
= $60
Answer(s): (a) $50; (b) $60