The ratio of the amount of money Cathy had to the amount of money Shiyun had was 6 : 7. Cathy then gave
56 of her money to Shiyun. In the end, Shiyun returned $77 to Cathy and they both had the same amount of money. How much money did each girl have at the beginning?
- Shiyun
- Cathy
|
Cathy |
Shiyun |
Total |
Before |
6 u |
7 u |
13 u |
Change 1 |
- 5 u |
+ 5 u |
|
After 1 |
1 u |
12 u |
13 u |
Change 2 |
+ 77 |
- 77 |
|
After 2 |
1 u + 77 |
12 u - 77 |
|
Amount that Cathy and Shiyun each had in the end is the same.
12 u - 77 = 1 u + 77
12 u - 1 u = 77 + 77
11 u = 154
1 u = 154 ÷ 11 = 14
Amount that Cathy had at first
= 6 u
= 6 x 14
= $84
(b)
Amount that Shiyun had at first
= 7 u
= 7 x 14
= $98
Answer(s): (a) $84; (b) $98