Fabian and Zoe has some money each. If Zoe gives Fabian $12, he will have 5 times as much money as her. If Fabian gives Zoe $19, he will have the same amount of money as her. How much money does each person have respectively?
- Fabian?
- Zoe?
|
Case 1 |
Case 2 |
|
Fabian |
Zoe |
Fabian |
Zoe |
Before |
5 u - 12 |
1 u + 12 |
3 u + 19 |
3 u - 19 |
Change |
+ 12 |
- 12 |
- 19 |
+ 19 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Zoe gives Fabian some money or Fabian gives Zoe some money, the total amount of money remains the same.
Total amount that Fabian and Zoe have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Fabian and Zoe each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Fabian has at first in Case 1 and Case 2 is the same.
5 u - 12 = 3 u + 19
5 u - 3 u = 19 + 12
1 u = 31
Amount that Fabian has
= 3 u + 19
= 3 x 31 + 19
= 93 + 19
= $112
(b)
Amount that Zoe has
= 1 u + 12
= 31 + 12
= $43
Answer(s): (a) $112; (b) $43