Valen and Xandra has some money each. If Xandra gives Valen $15, he will have 5 times as much money as her. If Valen gives Xandra $17, he will have the same amount of money as her. How much money does each person have respectively?
- Valen?
- Xandra?
| |
Case 1 |
Case 2 |
| |
Valen |
Xandra |
Valen |
Xandra |
| Before |
5 u - 15 |
1 u + 15 |
3 u + 17 |
3 u - 17 |
| Change |
+ 15 |
- 15 |
- 17 |
+ 17 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Xandra gives Valen some money or Valen gives Xandra some money, the total amount of money remains the same.
Total amount that Valen and Xandra have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Valen and Xandra each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Valen has at first in Case 1 and Case 2 is the same.
5 u - 15 = 3 u + 17
5 u - 3 u = 17 + 15
1 u = 32
Amount that Valen has
= 3 u + 17
= 3 x 32 + 17
= 96 + 17
= $113
(b)
Amount that Xandra has
= 1 u + 15
= 32 + 15
= $47
Answer(s): (a) $113; (b) $47
