Owen and Nicole has some money each. If Nicole gives Owen $16, he will have 3 times as much money as her. If Owen gives Nicole $14, he will have the same amount of money as her. How much money does each person have respectively?
- Owen?
- Nicole?
|
Case 1 |
Case 2 |
|
Owen |
Nicole |
Owen |
Nicole |
Before |
3 u - 16 |
1 u + 16 |
2 u + 14 |
2 u - 14 |
Change |
+ 16 |
- 16 |
- 14 |
+ 14 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Nicole gives Owen some money or Owen gives Nicole some money, the total amount of money remains the same.
Total amount that Owen and Nicole have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Owen and Nicole each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Owen has at first in Case 1 and Case 2 is the same.
3 u - 16 = 2 u + 14
3 u - 2 u = 14 + 16
1 u = 30
Amount that Owen has
= 2 u + 14
= 2 x 30 + 14
= 60 + 14
= $74
(b)
Amount that Nicole has
= 1 u + 16
= 30 + 16
= $46
Answer(s): (a) $74; (b) $46