Fabian and Cathy has some money each. If Cathy gives Fabian $10, he will have 7 times as much money as her. If Fabian gives Cathy $13, he will have the same amount of money as her. How much money does each person have respectively?
- Fabian?
- Cathy?
|
Case 1 |
Case 2 |
|
Fabian |
Cathy |
Fabian |
Cathy |
Before |
7 u - 10 |
1 u + 10 |
4 u + 13 |
4 u - 13 |
Change |
+ 10 |
- 10 |
- 13 |
+ 13 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Cathy gives Fabian some money or Fabian gives Cathy some money, the total amount of money remains the same.
Total amount that Fabian and Cathy have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Fabian and Cathy each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Fabian has at first in Case 1 and Case 2 is the same.
7 u - 10 = 4 u + 13
7 u - 4 u = 13 + 10
1 u = 23
Amount that Fabian has
= 4 u + 13
= 4 x 23 + 13
= 92 + 13
= $105
(b)
Amount that Cathy has
= 1 u + 10
= 23 + 10
= $33
Answer(s): (a) $105; (b) $33