The ratio of the amount of money Shannon had to the amount of money Betty had was 4 : 5. Shannon then gave
34 of her money to Betty. In the end, Betty returned $42 to Shannon and they both had the same amount of money. How much money did each girl have at the beginning?
- Betty
- Shannon
|
Shannon |
Betty |
Total |
Before |
4 u |
5 u |
9 u |
Change 1 |
- 3 u |
+ 3 u |
|
After 1 |
1 u |
8 u |
9 u |
Change 2 |
+ 42 |
- 42 |
|
After 2 |
1 u + 42 |
8 u - 42 |
|
Amount that Shannon and Betty each had in the end is the same.
8 u - 42 = 1 u + 42
8 u - 1 u = 42 + 42
7 u = 84
1 u = 84 ÷ 7 = 12
Amount that Shannon had at first
= 4 u
= 4 x 12
= $48
(b)
Amount that Betty had at first
= 5 u
= 5 x 12
= $60
Answer(s): (a) $48; (b) $60