Albert and Jane has some money each. If Jane gives Albert $12, he will have 3 times as much money as her. If Albert gives Jane $10, he will have the same amount of money as her. How much money does each person have respectively?
- Albert?
- Jane?
|
Case 1 |
Case 2 |
|
Albert |
Jane |
Albert |
Jane |
Before |
3 u - 12 |
1 u + 12 |
2 u + 10 |
2 u - 10 |
Change |
+ 12 |
- 12 |
- 10 |
+ 10 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Jane gives Albert some money or Albert gives Jane some money, the total amount of money remains the same.
Total amount that Albert and Jane have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Albert and Jane each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Albert has at first in Case 1 and Case 2 is the same.
3 u - 12 = 2 u + 10
3 u - 2 u = 10 + 12
1 u = 22
Amount that Albert has
= 2 u + 10
= 2 x 22 + 10
= 44 + 10
= $54
(b)
Amount that Jane has
= 1 u + 12
= 22 + 12
= $34
Answer(s): (a) $54; (b) $34