Fred and Zoe has some money each. If Zoe gives Fred $20, he will have 5 times as much money as her. If Fred gives Zoe $16, he will have the same amount of money as her. How much money does each person have respectively?
- Fred?
- Zoe?
|
Case 1 |
Case 2 |
|
Fred |
Zoe |
Fred |
Zoe |
Before |
5 u - 20 |
1 u + 20 |
3 u + 16 |
3 u - 16 |
Change |
+ 20 |
- 20 |
- 16 |
+ 16 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Zoe gives Fred some money or Fred gives Zoe some money, the total amount of money remains the same.
Total amount that Fred and Zoe have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Fred and Zoe each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Fred has at first in Case 1 and Case 2 is the same.
5 u - 20 = 3 u + 16
5 u - 3 u = 16 + 20
1 u = 36
Amount that Fred has
= 3 u + 16
= 3 x 36 + 16
= 108 + 16
= $124
(b)
Amount that Zoe has
= 1 u + 20
= 36 + 20
= $56
Answer(s): (a) $124; (b) $56