Seth and Esther has some money each. If Esther gives Seth $17, he will have 3 times as much money as her. If Seth gives Esther $13, he will have the same amount of money as her. How much money does each person have respectively?
- Seth?
- Esther?
|
Case 1 |
Case 2 |
|
Seth |
Esther |
Seth |
Esther |
Before |
3 u - 17 |
1 u + 17 |
2 u + 13 |
2 u - 13 |
Change |
+ 17 |
- 17 |
- 13 |
+ 13 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Esther gives Seth some money or Seth gives Esther some money, the total amount of money remains the same.
Total amount that Seth and Esther have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Seth and Esther each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Seth has at first in Case 1 and Case 2 is the same.
3 u - 17 = 2 u + 13
3 u - 2 u = 13 + 17
1 u = 30
Amount that Seth has
= 2 u + 13
= 2 x 30 + 13
= 60 + 13
= $73
(b)
Amount that Esther has
= 1 u + 17
= 30 + 17
= $47
Answer(s): (a) $73; (b) $47