Carl and Diana has some money each. If Diana gives Carl $12, he will have 3 times as much money as her. If Carl gives Diana $20, he will have the same amount of money as her. How much money does each person have respectively?
- Carl?
- Diana?
|
Case 1 |
Case 2 |
|
Carl |
Diana |
Carl |
Diana |
Before |
3 u - 12 |
1 u + 12 |
2 u + 20 |
2 u - 20 |
Change |
+ 12 |
- 12 |
- 20 |
+ 20 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Diana gives Carl some money or Carl gives Diana some money, the total amount of money remains the same.
Total amount that Carl and Diana have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Carl and Diana each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Carl has at first in Case 1 and Case 2 is the same.
3 u - 12 = 2 u + 20
3 u - 2 u = 20 + 12
1 u = 32
Amount that Carl has
= 2 u + 20
= 2 x 32 + 20
= 64 + 20
= $84
(b)
Amount that Diana has
= 1 u + 12
= 32 + 12
= $44
Answer(s): (a) $84; (b) $44