George and Erika has some money each. If Erika gives George $20, he will have 3 times as much money as her. If George gives Erika $10, he will have the same amount of money as her. How much money does each person have respectively?
- George?
- Erika?
|
Case 1 |
Case 2 |
|
George |
Erika |
George |
Erika |
Before |
3 u - 20 |
1 u + 20 |
2 u + 10 |
2 u - 10 |
Change |
+ 20 |
- 20 |
- 10 |
+ 10 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Erika gives George some money or George gives Erika some money, the total amount of money remains the same.
Total amount that George and Erika have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that George and Erika each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that George has at first in Case 1 and Case 2 is the same.
3 u - 20 = 2 u + 10
3 u - 2 u = 10 + 20
1 u = 30
Amount that George has
= 2 u + 10
= 2 x 30 + 10
= 60 + 10
= $70
(b)
Amount that Erika has
= 1 u + 20
= 30 + 20
= $50
Answer(s): (a) $70; (b) $50