Nick and Xandra has some money each. If Xandra gives Nick $11, he will have 5 times as much money as her. If Nick gives Xandra $12, he will have the same amount of money as her. How much money does each person have respectively?
- Nick?
- Xandra?
|
Case 1 |
Case 2 |
|
Nick |
Xandra |
Nick |
Xandra |
Before |
5 u - 11 |
1 u + 11 |
3 u + 12 |
3 u - 12 |
Change |
+ 11 |
- 11 |
- 12 |
+ 12 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Xandra gives Nick some money or Nick gives Xandra some money, the total amount of money remains the same.
Total amount that Nick and Xandra have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Nick and Xandra each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Nick has at first in Case 1 and Case 2 is the same.
5 u - 11 = 3 u + 12
5 u - 3 u = 12 + 11
1 u = 23
Amount that Nick has
= 3 u + 12
= 3 x 23 + 12
= 69 + 12
= $81
(b)
Amount that Xandra has
= 1 u + 11
= 23 + 11
= $34
Answer(s): (a) $81; (b) $34