Billy and Xandra has some money each. If Xandra gives Billy $17, he will have 3 times as much money as her. If Billy gives Xandra $13, he will have the same amount of money as her. How much money does each person have respectively?
- Billy?
- Xandra?
| |
Case 1 |
Case 2 |
| |
Billy |
Xandra |
Billy |
Xandra |
| Before |
3 u - 17 |
1 u + 17 |
2 u + 13 |
2 u - 13 |
| Change |
+ 17 |
- 17 |
- 13 |
+ 13 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Xandra gives Billy some money or Billy gives Xandra some money, the total amount of money remains the same.
Total amount that Billy and Xandra have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Billy and Xandra each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Billy has at first in Case 1 and Case 2 is the same.
3 u - 17 = 2 u + 13
3 u - 2 u = 13 + 17
1 u = 30
Amount that Billy has
= 2 u + 13
= 2 x 30 + 13
= 60 + 13
= $73
(b)
Amount that Xandra has
= 1 u + 17
= 30 + 17
= $47
Answer(s): (a) $73; (b) $47
