Archie and Ivory has some money each. If Ivory gives Archie $18, he will have 3 times as much money as her. If Archie gives Ivory $16, he will have the same amount of money as her. How much money does each person have respectively?
- Archie?
- Ivory?
|
Case 1 |
Case 2 |
|
Archie |
Ivory |
Archie |
Ivory |
Before |
3 u - 18 |
1 u + 18 |
2 u + 16 |
2 u - 16 |
Change |
+ 18 |
- 18 |
- 16 |
+ 16 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Ivory gives Archie some money or Archie gives Ivory some money, the total amount of money remains the same.
Total amount that Archie and Ivory have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Archie and Ivory each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Archie has at first in Case 1 and Case 2 is the same.
3 u - 18 = 2 u + 16
3 u - 2 u = 16 + 18
1 u = 34
Amount that Archie has
= 2 u + 16
= 2 x 34 + 16
= 68 + 16
= $84
(b)
Amount that Ivory has
= 1 u + 18
= 34 + 18
= $52
Answer(s): (a) $84; (b) $52