Nick and Tina has some money each. If Tina gives Nick $16, he will have 7 times as much money as her. If Nick gives Tina $10, he will have the same amount of money as her. How much money does each person have respectively?
- Nick?
- Tina?
|
Case 1 |
Case 2 |
|
Nick |
Tina |
Nick |
Tina |
Before |
7 u - 16 |
1 u + 16 |
4 u + 10 |
4 u - 10 |
Change |
+ 16 |
- 16 |
- 10 |
+ 10 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Tina gives Nick some money or Nick gives Tina some money, the total amount of money remains the same.
Total amount that Nick and Tina have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Nick and Tina each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Nick has at first in Case 1 and Case 2 is the same.
7 u - 16 = 4 u + 10
7 u - 4 u = 10 + 16
1 u = 26
Amount that Nick has
= 4 u + 10
= 4 x 26 + 10
= 104 + 10
= $114
(b)
Amount that Tina has
= 1 u + 16
= 26 + 16
= $42
Answer(s): (a) $114; (b) $42