Vincent and Zoe has some money each. If Zoe gives Vincent $12, he will have 5 times as much money as her. If Vincent gives Zoe $14, he will have the same amount of money as her. How much money does each person have respectively?
- Vincent?
- Zoe?
|
Case 1 |
Case 2 |
|
Vincent |
Zoe |
Vincent |
Zoe |
Before |
5 u - 12 |
1 u + 12 |
3 u + 14 |
3 u - 14 |
Change |
+ 12 |
- 12 |
- 14 |
+ 14 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Zoe gives Vincent some money or Vincent gives Zoe some money, the total amount of money remains the same.
Total amount that Vincent and Zoe have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Vincent and Zoe each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Vincent has at first in Case 1 and Case 2 is the same.
5 u - 12 = 3 u + 14
5 u - 3 u = 14 + 12
1 u = 26
Amount that Vincent has
= 3 u + 14
= 3 x 26 + 14
= 78 + 14
= $92
(b)
Amount that Zoe has
= 1 u + 12
= 26 + 12
= $38
Answer(s): (a) $92; (b) $38