Carl and Tina has some money each. If Tina gives Carl $16, he will have 5 times as much money as her. If Carl gives Tina $17, he will have the same amount of money as her. How much money does each person have respectively?
- Carl?
- Tina?
| |
Case 1 |
Case 2 |
| |
Carl |
Tina |
Carl |
Tina |
| Before |
5 u - 16 |
1 u + 16 |
3 u + 17 |
3 u - 17 |
| Change |
+ 16 |
- 16 |
- 17 |
+ 17 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Tina gives Carl some money or Carl gives Tina some money, the total amount of money remains the same.
Total amount that Carl and Tina have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Carl and Tina each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Carl has at first in Case 1 and Case 2 is the same.
5 u - 16 = 3 u + 17
5 u - 3 u = 17 + 16
1 u = 33
Amount that Carl has
= 3 u + 17
= 3 x 33 + 17
= 99 + 17
= $116
(b)
Amount that Tina has
= 1 u + 16
= 33 + 16
= $49
Answer(s): (a) $116; (b) $49
