Carl and Tiffany has some money each. If Tiffany gives Carl $18, he will have 5 times as much money as her. If Carl gives Tiffany $12, he will have the same amount of money as her. How much money does each person have respectively?
- Carl?
- Tiffany?
| |
Case 1 |
Case 2 |
| |
Carl |
Tiffany |
Carl |
Tiffany |
| Before |
5 u - 18 |
1 u + 18 |
3 u + 12 |
3 u - 12 |
| Change |
+ 18 |
- 18 |
- 12 |
+ 12 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Tiffany gives Carl some money or Carl gives Tiffany some money, the total amount of money remains the same.
Total amount that Carl and Tiffany have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Carl and Tiffany 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 - 18 = 3 u + 12
5 u - 3 u = 12 + 18
1 u = 30
Amount that Carl has
= 3 u + 12
= 3 x 30 + 12
= 90 + 12
= $102
(b)
Amount that Tiffany has
= 1 u + 18
= 30 + 18
= $48
Answer(s): (a) $102; (b) $48
