Peter and Vanessa has some money each. If Vanessa gives Peter $13, he will have 3 times as much money as her. If Peter gives Vanessa $20, he will have the same amount of money as her. How much money does each person have respectively?
- Peter?
- Vanessa?
|
Case 1 |
Case 2 |
|
Peter |
Vanessa |
Peter |
Vanessa |
Before |
3 u - 13 |
1 u + 13 |
2 u + 20 |
2 u - 20 |
Change |
+ 13 |
- 13 |
- 20 |
+ 20 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Vanessa gives Peter some money or Peter gives Vanessa some money, the total amount of money remains the same.
Total amount that Peter and Vanessa have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Peter and Vanessa each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Peter has at first in Case 1 and Case 2 is the same.
3 u - 13 = 2 u + 20
3 u - 2 u = 20 + 13
1 u = 33
Amount that Peter has
= 2 u + 20
= 2 x 33 + 20
= 66 + 20
= $86
(b)
Amount that Vanessa has
= 1 u + 13
= 33 + 13
= $46
Answer(s): (a) $86; (b) $46