Archie and Jane has some money each. If Jane gives Archie $11, he will have 3 times as much money as her. If Archie gives Jane $17, he will have the same amount of money as her. How much money does each person have respectively?
- Archie?
- Jane?
| |
Case 1 |
Case 2 |
| |
Archie |
Jane |
Archie |
Jane |
| Before |
3 u - 11 |
1 u + 11 |
2 u + 17 |
2 u - 17 |
| Change |
+ 11 |
- 11 |
- 17 |
+ 17 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Jane gives Archie some money or Archie gives Jane some money, the total amount of money remains the same.
Total amount that Archie and Jane have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Archie and Jane 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 - 11 = 2 u + 17
3 u - 2 u = 17 + 11
1 u = 28
Amount that Archie has
= 2 u + 17
= 2 x 28 + 17
= 56 + 17
= $73
(b)
Amount that Jane has
= 1 u + 11
= 28 + 11
= $39
Answer(s): (a) $73; (b) $39
