Carl and Gillian has some money each. If Gillian gives Carl $10, he will have 5 times as much money as her. If Carl gives Gillian $16, he will have the same amount of money as her. How much money does each person have respectively?
- Carl?
- Gillian?
|
Case 1 |
Case 2 |
|
Carl |
Gillian |
Carl |
Gillian |
Before |
5 u - 10 |
1 u + 10 |
3 u + 16 |
3 u - 16 |
Change |
+ 10 |
- 10 |
- 16 |
+ 16 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Gillian gives Carl some money or Carl gives Gillian some money, the total amount of money remains the same.
Total amount that Carl and Gillian have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Carl and Gillian 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 - 10 = 3 u + 16
5 u - 3 u = 16 + 10
1 u = 26
Amount that Carl has
= 3 u + 16
= 3 x 26 + 16
= 78 + 16
= $94
(b)
Amount that Gillian has
= 1 u + 10
= 26 + 10
= $36
Answer(s): (a) $94; (b) $36