Fred and Vanessa has some money each. If Vanessa gives Fred $14, he will have 5 times as much money as her. If Fred gives Vanessa $18, he will have the same amount of money as her. How much money does each person have respectively?
- Fred?
- Vanessa?
| |
Case 1 |
Case 2 |
| |
Fred |
Vanessa |
Fred |
Vanessa |
| Before |
5 u - 14 |
1 u + 14 |
3 u + 18 |
3 u - 18 |
| Change |
+ 14 |
- 14 |
- 18 |
+ 18 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Vanessa gives Fred some money or Fred gives Vanessa some money, the total amount of money remains the same.
Total amount that Fred and Vanessa have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Fred and Vanessa 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 - 14 = 3 u + 18
5 u - 3 u = 18 + 14
1 u = 32
Amount that Fred has
= 3 u + 18
= 3 x 32 + 18
= 96 + 18
= $114
(b)
Amount that Vanessa has
= 1 u + 14
= 32 + 14
= $46
Answer(s): (a) $114; (b) $46
