Caden and Ivory has some money each. If Ivory gives Caden $10, he will have 3 times as much money as her. If Caden gives Ivory $14, he will have the same amount of money as her. How much money does each person have respectively?
- Caden?
- Ivory?
| |
Case 1 |
Case 2 |
| |
Caden |
Ivory |
Caden |
Ivory |
| Before |
3 u - 10 |
1 u + 10 |
2 u + 14 |
2 u - 14 |
| Change |
+ 10 |
- 10 |
- 14 |
+ 14 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Ivory gives Caden some money or Caden gives Ivory some money, the total amount of money remains the same.
Total amount that Caden and Ivory have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Caden and Ivory each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Caden has at first in Case 1 and Case 2 is the same.
3 u - 10 = 2 u + 14
3 u - 2 u = 14 + 10
1 u = 24
Amount that Caden has
= 2 u + 14
= 2 x 24 + 14
= 48 + 14
= $62
(b)
Amount that Ivory has
= 1 u + 10
= 24 + 10
= $34
Answer(s): (a) $62; (b) $34
